Given the small bit allocation for motion information in very low bit-rate coding, motion estimation using the block matching algorithm (BMA) fails to maintain an acceptable level of prediction errors. The reason is that the motion model, or spatial transformation, assumed in block matching cannot approximate the motion in the real world precisely with a small number of parameters. In order to overcome the drawback of the conventional block matching algorithm, several triangle-based methods which utilize triangular patches instead of blocks have been proposed. To estimate the motions of image sequences, these methods usually have been based on the combination of optical flow equation, affine transform, and iteration. But the computational cost of these methods is expensive. This paper presents a fast motion estimation algorithm suing a multiple linear regression model to solve the defects of the BMA and the triangle-based methods. After describing the basic 2D triangle-based method, the details of the proposed multiple linear regression model are presented along with the motion estimation results from one standard video sequence, representative of MPEG-4 class A data. The simulation results show that in the proposed method, the average PSNR is improved about 1.24 dB in comparison with the BMA method, and the computational cost is reduced about 40 percent in comparison with the 2D triangle-based method.