diff --git a/src/QCQP/MOI_wrapper.jl b/src/QCQP/MOI_wrapper.jl
index 463c93a..35b666d 100644
--- a/src/QCQP/MOI_wrapper.jl
+++ b/src/QCQP/MOI_wrapper.jl
@@ -198,6 +198,16 @@ function MOI.supports_constraint(
     )
 end
 
+function MOI.get(
+    model::Optimizer{T},
+    ::MOI.ConstraintBridgingCost{<:PolyJuMP.ScalarPolynomialFunction{T},S},
+) where {T,S<:MOI.AbstractScalarSet}
+    return MOI.get(
+        model.model,
+        MOI.ConstraintBridgingCost{MOI.ScalarQuadraticFunction{T},S}(),
+    )
+end
+
 function MOI.add_constraint(
     model::Optimizer,
     func::MOI.AbstractFunction,
diff --git a/test/qcqp.jl b/test/qcqp.jl
index 3a517e7..f190061 100644
--- a/test/qcqp.jl
+++ b/test/qcqp.jl
@@ -373,6 +373,26 @@ function test_inner_bridge(x, y, T)
           MOI.get(inner, MOI.ListOfModelAttributesSet())
 end
 
+function test_constraint_bridging_cost_polynomial(x, y, T)
+    inner = MOI.Utilities.MockOptimizer(Model{T}())
+    optimizer = PolyJuMP.QCQP.Optimizer{T}(inner)
+    F = typeof(
+        PolyJuMP.ScalarPolynomialFunction(
+            one(T) * x^3 - x * y^2,
+            [MOI.VariableIndex(1), MOI.VariableIndex(2)],
+        ),
+    )
+    for S in
+        (MOI.LessThan{T}, MOI.GreaterThan{T}, MOI.EqualTo{T}, MOI.Interval{T})
+        @test MOI.supports_constraint(optimizer, F, S)
+        @test MOI.get(optimizer, MOI.ConstraintBridgingCost{F,S}()) == MOI.get(
+            optimizer,
+            MOI.ConstraintBridgingCost{MOI.ScalarQuadraticFunction{T},S}(),
+        )
+    end
+    return
+end
+
 function runtests(x, y)
     for name in names(@__MODULE__; all = true)
         if startswith("$name", "test_")