Abstract: In this paper,   sequential block-iterative subgradient projection algorithm and parallel block-iterative subgradient projection algorithm for solving the convex feasibility problem expressed by  the system of inequalities are presented. Each step in these methods consists of finding the approximation projection of the current point on the subsystem which is constructed  through  parting  the system of inequalities into several blocks.  The convergence for both of sequential block-iterative subgradient projection algorithm and parallel block-iterative subgradient projection algorithm are obtained under some weak conditions.