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diff --git a/‎doc/whats_new/v1.2.rst
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diff --git a/‎sklearn/ensemble/_weight_boosting.py
Lines changed: 8 additions & 1 deletion b/‎sklearn/ensemble/_weight_boosting.py
Lines changed: 8 additions & 1 deletion
diff --git a/‎sklearn/ensemble/tests/test_weight_boosting.py
Lines changed: 20 additions & 1 deletion b/‎sklearn/ensemble/tests/test_weight_boosting.py
Lines changed: 20 additions & 1 deletion
@@ -183,6 +183,13 @@ Changelog
 - |Efficiency| Improve runtime performance of :class:`ensemble.IsolationForest`
   by avoiding data copies. :pr:`23252` by :user:`Zhehao Liu <MaxwellLZH>`.
 
+- |Fix| Fixed the issue where :class:`ensemble.AdaBoostClassifier` outputs
+  NaN in feature importance when fitted with very small sample weight.
+  :pr:`20415` by :user:`Zhehao Liu <MaxwellLZH>`.
+
+:mod:`sklearn.feature_selection`
+................................
+
 :mod:`sklearn.decomposition`
 ............................
 
 
@@ -146,8 +146,15 @@ def fit(self, X, y, sample_weight=None):
         # Initialization of the random number instance that will be used to
         # generate a seed at each iteration
         random_state = check_random_state(self.random_state)
+        epsilon = np.finfo(sample_weight.dtype).eps
 
+        zero_weight_mask = sample_weight == 0.0
         for iboost in range(self.n_estimators):
+            # avoid extremely small sample weight, for details see issue #20320
+            sample_weight = np.clip(sample_weight, a_min=epsilon, a_max=None)
+            # do not clip sample weights that were exactly zero originally
+            sample_weight[zero_weight_mask] = 0.0
+
             # Boosting step
             sample_weight, estimator_weight, estimator_error = self._boost(
                 iboost, X, y, sample_weight, random_state
@@ -635,7 +642,7 @@ def _boost_discrete(self, iboost, X, y, sample_weight, random_state):
             np.log((1.0 - estimator_error) / estimator_error) + np.log(n_classes - 1.0)
         )
 
-        # Only boost the weights if I will fit again
+        # Only boost the weights if it will fit again
         if not iboost == self.n_estimators - 1:
             # Only boost positive weights
             sample_weight = np.exp(
 
@@ -309,7 +309,7 @@ def test_base_estimator():
 
 def test_sample_weights_infinite():
     msg = "Sample weights have reached infinite values"
-    clf = AdaBoostClassifier(n_estimators=30, learning_rate=5.0, algorithm="SAMME")
+    clf = AdaBoostClassifier(n_estimators=30, learning_rate=23.0, algorithm="SAMME")
     with pytest.warns(UserWarning, match=msg):
         clf.fit(iris.data, iris.target)
 
@@ -575,3 +575,22 @@ def test_adaboost_negative_weight_error(model, X, y):
     err_msg = "Negative values in data passed to `sample_weight`"
     with pytest.raises(ValueError, match=err_msg):
         model.fit(X, y, sample_weight=sample_weight)
+
+
+def test_adaboost_numerically_stable_feature_importance_with_small_weights():
+    """Check that we don't create NaN feature importance with numerically
+    instable inputs.
+
+    Non-regression test for:
+    https://github.com/scikit-learn/scikit-learn/issues/20320
+    """
+    rng = np.random.RandomState(42)
+    X = rng.normal(size=(1000, 10))
+    y = rng.choice([0, 1], size=1000)
+    sample_weight = np.ones_like(y) * 1e-263
+    tree = DecisionTreeClassifier(max_depth=10, random_state=12)
+    ada_model = AdaBoostClassifier(
+        base_estimator=tree, n_estimators=20, random_state=12
+    )
+    ada_model.fit(X, y, sample_weight=sample_weight)
+    assert np.isnan(ada_model.feature_importances_).sum() == 0