L1-regularized least squares, with the ability of discovering sparse representations, is quite prevalent in the field of machine learning, statistics and signal processing. In this paper, we propose a novel algorithm called Dual Projected Newton Method (DPNM) to solve the L1-regularized least squares problem. In DPNM, we first derive a new dual problem as a box constrained quadratic programming. Then, a projected Newton method is utilized to solve the dual problem, achieving a quadratic convergence rate. Moreover, we propose to utilize some practical techniques, thus it greatly reduces the computational cost and makes DPNM more efficient. Experimental results on six real-world data sets indicate that DPNM is very efficient for solving the L1-regularized least squares problem, by comparing it with state of the art methods.