An efficient algorithm for overcomplete dictionary learning with l_p-norm as sparsity constraint to achieve sparse representation from a set of known signals is presented in this paper. The special importance of the l_p-norm (0<p<1) has been recognized in recent studies on sparse modeling, which can lead to stronger sparsity-promoting solutions than the l_1-norm. The l_p-norm, however, leads to a nonconvex optimization problem that is difficult to solve efficiently. In this paper, the hierarchically alternating update strategy and the weighted l_1-norm method are introduced to the learning procedure which find local optimal at each iteration. This algorithm is validated to be effective in numerical experiments and present the advantages in recovery ratios of dictionary and robustness of noise compared to MOD, K-SVD and FOCUSS-CNDL.