diff --git a/onnxmltools/convert/xgboost/common.py b/onnxmltools/convert/xgboost/common.py
index 4a10a48f..8b8fd1a3 100644
--- a/onnxmltools/convert/xgboost/common.py
+++ b/onnxmltools/convert/xgboost/common.py
@@ -29,9 +29,16 @@ def get_xgb_params(xgb_node):
         if xgb_node.n_estimators is not None:
             params["n_estimators"] = xgb_node.n_estimators
     if "base_score" in config["learner"]["learner_model_param"]:
-        bs = float(config["learner"]["learner_model_param"]["base_score"])
-        # xgboost >= 2.0
-        params["base_score"] = bs
+         base_score = config["learner"]["learner_model_param"]["base_score"]
+         if(base_score.startswith('[') and base_score.endswith(']')):
+            # xgboost >= 3.1, see 
+            base_score = [float(score) for score in base_score.strip('[]').split(',')]
+            if len(base_score) == 1:
+                base_score = base_score[0]
+         else:
+            #xgboost >= 2.0 and < 3.1
+            base_score = float(base_score)
+         params["base_score"] = base_score
     if "num_target" in config["learner"]["learner_model_param"]:
         params["n_targets"] = int(
             config["learner"]["learner_model_param"]["num_target"]
@@ -48,6 +55,11 @@ def get_xgb_params(xgb_node):
             params["best_ntree_limit"] = int(gbp["num_trees"])
     return params
 
+def base_score_as_list(base_score):
+    if isinstance(base_score, list):
+        return base_score
+    return [base_score]
+
 
 def get_n_estimators_classifier(xgb_node, params, js_trees):
     if "n_estimators" not in params:
diff --git a/onnxmltools/convert/xgboost/operator_converters/XGBoost.py b/onnxmltools/convert/xgboost/operator_converters/XGBoost.py
index aeec4364..3797d40a 100644
--- a/onnxmltools/convert/xgboost/operator_converters/XGBoost.py
+++ b/onnxmltools/convert/xgboost/operator_converters/XGBoost.py
@@ -10,7 +10,7 @@
 except ImportError:
     XGBRFClassifier = None
 from ...common._registration import register_converter
-from ..common import get_xgb_params, get_n_estimators_classifier
+from ..common import get_xgb_params, get_n_estimators_classifier, base_score_as_list
 
 
 class XGBConverter:
@@ -259,7 +259,7 @@ def convert(scope, operator, container):
             raise RuntimeError("Objective '{}' not supported.".format(objective))
 
         attr_pairs = XGBRegressorConverter._get_default_tree_attribute_pairs()
-        attr_pairs["base_values"] = [base_score]
+        attr_pairs["base_values"] = base_score_as_list(base_score)
 
         if best_ntree_limit and best_ntree_limit < len(js_trees):
             js_trees = js_trees[:best_ntree_limit]
@@ -350,17 +350,20 @@ def convert(scope, operator, container):
                 attr_pairs["post_transform"] = "LOGISTIC"
                 attr_pairs["class_ids"] = [0 for v in attr_pairs["class_treeids"]]
                 if js_trees[0].get("leaf", None) == 0:
-                    attr_pairs["base_values"] = [base_score]
+                    attr_pairs["base_values"] = base_score_as_list(base_score)
                 elif base_score != 0.5:
                     # 0.5 -> cst = 0
-                    cst = -np.log(1 / np.float32(base_score) - 1.0)
-                    attr_pairs["base_values"] = [cst]
+                    cst = -np.log(1 / np.array(base_score_as_list(base_score), dtype=np.float32) - 1.0)
+                    attr_pairs["base_values"] = cst.tolist()
             else:
-                attr_pairs["base_values"] = [base_score]
+                attr_pairs["base_values"] = base_score_as_list(base_score)
         else:
             # See https://github.com/dmlc/xgboost/blob/main/src/common/math.h#L35.
             attr_pairs["post_transform"] = "SOFTMAX"
-            attr_pairs["base_values"] = [base_score for n in range(ncl)]
+            if isinstance(base_score, list):
+                attr_pairs["base_values"] = base_score
+            else:
+                attr_pairs["base_values"] = [base_score for n in range(ncl)]
             attr_pairs["class_ids"] = [v % ncl for v in attr_pairs["class_treeids"]]
 
         classes = xgb_node.classes_