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 lp-norm minimization.