Summary: Conventional sparse signal recovery algorithms fail to promote strong sparsity. To overcome this drawback, this paper proposes a sparse signal recovery algorithm based on a non-convex function with enhanced sparsity. Relationship between the shrinkage function and the penalty function is shown, and a new non-convex penalty function with enhanced sparsity is proposed. The majorization-minimization (MM) method is used to solve the nonconvex optimization problem. The convex upper bounds are constructed to approximate the original non-convex penalty function that is hard to solve. Both the convex part and the convex upper bounds of this objective function are optimized iteratively. Compared with existing algorithms based on non-convex penalty functions, the proposed algorithm has two main advantages. First, it is free of the impact of parameter. Second, the gradient direction of the proposed algorithm includes the non-convex part of the objective function. In particular, for sparse wireless channel estimation problems, simulation shows that the proposed algorithm can achieve more accurate estimation with less pilot symbols.