In this paper we propose a centralized three-term conjugate gradient method for solving the variational inequality over the intersection of nonempty closed and convex constraints which are represented in the form of the fixed-point sets of firmly nonexpansive operators. The method allows not only computation of a single firmly nonexpansive operator, but also application in the situation when the computation of metric projection onto the constrained set cannot be done easily. Under some suitable conditions on corresponding parameters, we show a strong convergence of the iterate to the unique solution of such a variational inequality problem. Finally, in order to show the effectiveness of the theoretical result, we present some numerical experiments on the image classification problem via support vector machine learning.