In this paper, an efficient approximate VQ codeword search algorithm is proposed. This algorithm is based on a modification of the Chebyshev metric (or Manhattan metric). Applying this new algorithm to VQ codeword search and comparing it with the minimax method, it is found that more than 36% and 5% multiplications can be saved for 8 and 1024 codewords, respectively. In terms of the total number of mathematical operations, a few mathematical operations can be saved without inducing any extra distortion. Experimental results confirm this new algorithm.