diff --git a/sqlglot/dialects/postgres.py b/sqlglot/dialects/postgres.py
index 008727c6db..25c3601e22 100644
--- a/sqlglot/dialects/postgres.py
+++ b/sqlglot/dialects/postgres.py
@@ -439,6 +439,8 @@ class Generator(generator.Generator):
             exp.TryCast: no_trycast_sql,
             exp.TsOrDsToDate: ts_or_ds_to_date_sql("postgres"),
             exp.UnixToTime: lambda self, e: f"TO_TIMESTAMP({self.sql(e, 'this')})",
+            exp.VariancePop: rename_func("VAR_POP"),
+            exp.Variance: rename_func("VAR_SAMP"),
             exp.Xor: bool_xor_sql,
         }
 
diff --git a/tests/dialects/test_postgres.py b/tests/dialects/test_postgres.py
index 0ddc10613a..641c1ea841 100644
--- a/tests/dialects/test_postgres.py
+++ b/tests/dialects/test_postgres.py
@@ -724,3 +724,11 @@ def test_string_concat(self):
                 "presto": "CONCAT(CAST(a AS VARCHAR), CAST(b AS VARCHAR))",
             },
         )
+
+    def test_variance(self):
+        self.validate_all("VAR_SAMP(x)", write={"postgres": "VAR_SAMP(x)"})
+        self.validate_all("VAR_POP(x)", write={"postgres": "VAR_POP(x)"})
+        self.validate_all("VARIANCE(x)", write={"postgres": "VAR_SAMP(x)"})
+        self.validate_all(
+            "VAR_POP(x)", read={"": "VARIANCE_POP(x)"}, write={"postgres": "VAR_POP(x)"}
+        )