The author considers vector quantization that uses the L (1) distortion measure for its implementation. A gradient-based approach for codebook design that does not require any multiplications or median computation is proposed. Convergence of this method is proved rigorously under very mild conditions. Simulation examples comparing the performance of this technique with the LBG algorithm show that the gradient-based method, in spite of its simplicity, produces codebooks with average distortions that are comparable to the LBG algorithm. The codebook design algorithm is then extended to a distortion measure that has piecewise-linear characteristics. Once again, by appropriate selection of the parameters of the distortion measure, the encoding as well as the codebook design can be implemented with zero multiplications. The author applies the techniques in predictive vector quantization of images and demonstrates the viability of multiplication-free predictive vector quantization of image data.