In this paper, we consider unilateral contact problem without friction between a rigid body_and deformable one in the framework of isogeometric analysis. We present the theoretical_analysis of the mixed problem using an active-set strategy and for a primal space of NURBS_of degree $p$ and $p-2$ for a dual space of B-Spline. A inf--sup stability is proved to ensure_a good property of the method. An optimal a priori error estimate is demonstrated without_assumption on the unknown contact set. Several numerical examples in two- and threedimensional_and in small and large deformations demonstrate the accuracy of the proposed_method.