Data acquisition time is a bottle neck for increasing imaging speed of magnetic resonance imaging. To solve the problem, a new fast magnetic resonance imaging method based on variable-density spiral acquisition and Bregman iterative reconstruction is proposed in this paper, under the framework of compressed sensing. The proposed method increases the acquisition speed by data undersampling. The resulting undersampling aliasing artifact is removed by utilizing the intrinsic property of variable-density spiral and Bregman iterative recosntruction. The proposed method is validated by both phantom experiemnt and in vivo experiment. The experimental results demonstrate that the proposed method can effectively remove aliasing artifact from data undersampling, and achieve an image with well-preserved image structure information. Therefore this method can be used for reducing data acquisition time.