Dual energy computed tomography (DECT) has significant impacts on material characterization, bone mineral density inspection, nondestructive evaluation and so on. In spite of great progress has been made recently on reconstruction algorithms for DECT, there still exist two main problems: 1) For polyenergetic X-ray source, the tube spectrum needed in reconstruction is not always available. 2) The reconstructed image of DECT is very sensitive to noise which demands special noise suppression strategy in reconstruction algorithm design. In this paper, we propose a novel method for DECT reconstruction that reconstructs tube spectrum from projection data and suppresses image noise by introducing l(1)-norm based regularization into statistical reconstruction for polychromatic DECT. The contribution of this work is twofold. 1) A three parameters model is devised to represent spectrum of ployenergetic X-ray source. And the parameters can be estimated from projection data by solving an optimization problem. 2) With the estimated tube spectrum, we propose a computation framework of l(1)-norm regularization based statistical iterative reconstruction for polychromatic DECT. Simulation experiments with two phantoms were conducted to evaluate the proposed method. Experimental results demonstrate the accuracy and robustness of the spectrum model in terms of that comparable reconstruction image quality can be achieved with the estimated and ideal spectrum, and validate that the proposed method works with attractive performance in terms of accuracy of reconstructed image. The root mean square error (RMSE) between the reconstructed image and the ground truth image are 7.648 x 10(-4) and 2.687 x 10(-4) for the two phantoms, respectively.