In this paper we consider the level-boundedness of the natural residual function for the variational inequality problem (VIP). We first introduce the concept of strong coercivity for vector-valued mappings. The strong coercivity is related to the weak coercivity of vector-valued mappings and is weaker than the strong monotonicity of mappings. We show that the natural residual function
associated with VIP is level-bounded under the strong coercivity of the mapping involved in the VIP.