Aprojectedsubgradientmethodforsolvingaclassofset-valuedmixedvariationalinequalities(SMVIs)isproposedwhenthemappingisnotnecessarilyLipschitz.Undersomesuitableconditions,itcanbeproventhatthesequencegeneratedbythemethodcanstronglyconvergetotheuniquesolutiontotheproblemintheHilbertspaces.