In this paper we introduce a scalar gap function for a Stampacchia type vector variational inequality problem. We show how properties of the gap function can be improved by regularizing it in the sense of Fukushima. We study in detail the properties of this regularized gap function. An error bound for the vector variational inequality is obtained in terms of the regularized gap function. We also introduce the notion of D-gap function for vector variational inequalities. We study its properties and also present an error bound in terms of the D-gap functions. © 2010 Yokohama Publishers.