diff --git a/src/MOI_wrapper/MOI_nonlinear.jl b/src/MOI_wrapper/MOI_nonlinear.jl
index 8208802..976098c 100644
--- a/src/MOI_wrapper/MOI_nonlinear.jl
+++ b/src/MOI_wrapper/MOI_nonlinear.jl
@@ -206,15 +206,24 @@ function _add_expression_tree_node(
     append!(data, -1.0)
     append!(parent, parent_index)
     multiply_parent_index = Cint(length(opcode) - 1)
-    _add_expression_tree_node(
-        model,
-        stack,
-        opcode,
-        data,
-        parent,
-        term.coefficient,
-        multiply_parent_index,
-    )
+    # https://jump.dev/MathOptInterface.jl/stable/reference/standard_form
+    # ScalarQuadraticFunction stores diagonal ScalarQuadraticTerms multiplied by
+    # 2
+    coeff = term.coefficient
+    if term.variable_1 == term.variable_2
+        coeff /= 2
+    end
+    if !isone(coeff)
+        _add_expression_tree_node(
+            model,
+            stack,
+            opcode,
+            data,
+            parent,
+            coeff,
+            multiply_parent_index,
+        )
+    end
     _add_expression_tree_node(
         model,
         stack,
@@ -274,19 +283,13 @@ function _add_expression_tree_node(
         )
     end
     for term in s.quadratic_terms
-        # https://jump.dev/MathOptInterface.jl/stable/reference/standard_form
-        # ScalarQuadraticFunction stores ScalarQuadraticTerms multiplied by 2
         _add_expression_tree_node(
             model,
             stack,
             opcode,
             data,
             parent,
-            MOI.ScalarQuadraticTerm{Float64}(
-                0.5 * term.coefficient,
-                term.variable_1,
-                term.variable_2,
-            ),
+            term,
             plus_parent_index,
         )
     end
diff --git a/test/MOI/MOI_wrapper.jl b/test/MOI/MOI_wrapper.jl
index f841267..b8d43f5 100644
--- a/test/MOI/MOI_wrapper.jl
+++ b/test/MOI/MOI_wrapper.jl
@@ -1352,8 +1352,8 @@ function test_nonlinear_quadratic_3()
     MOI.set(model, MOI.ObjectiveSense(), MOI.MAX_SENSE)
     f = 1.0 * x + 1.0 * y
     MOI.set(model, MOI.ObjectiveFunction{typeof(f)}(), f)
-    f1 = MOI.ScalarQuadraticTerm{Float64}(1.0, x, x)
-    f2 = MOI.ScalarQuadraticTerm{Float64}(1.0, y, y)
+    f1 = MOI.ScalarQuadraticTerm{Float64}(2.0, x, x)
+    f2 = MOI.ScalarQuadraticTerm{Float64}(2.0, y, y)
     f3 = MOI.ScalarNonlinearFunction(:+, Any[f1, f2])
     g = MOI.ScalarNonlinearFunction(:sqrt, Any[f3])
     c = MOI.add_constraint(model, g, MOI.LessThan(1.0))
@@ -1456,6 +1456,28 @@ function test_delete_nonlinear_index()
     return
 end
 
+function test_scalar_quadratic_function_with_off_diag_in_scalar_nonlinear()
+    if !Gurobi._supports_nonlinear()
+        return
+    end
+    for (a, b, status) in [
+        (1.0, 2.0, MOI.OPTIMAL),
+        (1.0, 3.0, MOI.INFEASIBLE),
+        (2.0, 3.0, MOI.OPTIMAL),
+        (2.0, 4.0, MOI.INFEASIBLE),
+    ]
+        model = Gurobi.Optimizer(GRB_ENV)
+        MOI.set(model, MOI.Silent(), true)
+        x, _ = MOI.add_constrained_variable(model, MOI.EqualTo(2.0))
+        y, _ = MOI.add_constrained_variable(model, MOI.EqualTo(3.0))
+        f = MOI.ScalarNonlinearFunction(:sqrt, Any[a*x*y])
+        MOI.add_constraint(model, f, MOI.GreaterThan(b))
+        MOI.optimize!(model)
+        @test MOI.get(model, MOI.TerminationStatus()) == status
+    end
+    return
+end
+
 end  # TestMOIWrapper
 
 TestMOIWrapper.runtests()