In this paper we propose an L1/2 regularizer which has a nonconvex penalty. The L1/2 regularizer is shown to have many promising properties such as unbiasedness, sparsity and Oracle properties. A reweighed iterative algorithm is proposed so that the solution of the L1/2 regularizer can be solved through transforming it into the solution of a series of L1 regularizers. The solution of the L1/2 regularizer is more sparse than that of the L1 regularizer, while solving the L1/2 regularizer ismuch simpler than solving the L0 regularizer. The experiments show that the L1/2 regularizer is very useful and efficient, and can be taken as a representative of the Lp(0<p<1) regularizer.