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We propose a new sparsity-promoting objective function to be used in sparse signal recovery. Specifically, the objective is an entropy function l1 defined on the sparse signal x. Compared to the conventional l1, it is a nonconvex function and the optimization problem can be solved based on the fast iterative shrinkage thresholding algorithm (FISTA). Experiments on 1-dimensional sparse signal recovery and 2-dimensional real image recovery show that minimizing lp favors sparse solutions, and that it could recover sparse signals better than the convex l1 norm minimization and the nonconvex l p -norm minimization.