This paper is concerned with the L1/2 regularization problem. We first study the optimality conditions for the problem. The optimality conditions obtained are the extensions of the optimality conditions for the minimization of a smooth function. Based on this, we derive a decent direction.We then develop a descent method for solving the problem. The method can be regarded as an extension of the well-known steepest descent method. Under appropriate conditions, we show that the proposed method is globally convergent.