In this paper, we concern with the split feasibility problem (SFP) whenever the convex sets involved are composed of level sets. By applying Gradient-projection algorithm which is used to solve constrained convex minimization problem of a real valued convex function, we construct two new algorithms for the split feasibility problem and prove that both of them are convergent weakly to a solution of the feasibility problem. In the end, as an application, we obtain a new algorithm for solving the split equality problem.