This paper presents a novel competitive learning algorithm for the design of variable-rate vector quantizers (VQs). The algorithm, termed variable-rate competitive learning (VRCL) algorithm, designs a VQ having minimum average distortion subject to a rate constraint. The VRCL performs the weight vector training in the wavelet domain so that required training time is short. In addition, the algorithm enjoys a better rate-distortion performance than that of other existing VQ design algorithms and competitive learning algorithms. The learning algorithm is also more insensitive to the selection of initial codewords as compared with existing design algorithms. Therefore, the VRCL algorithm can be an effective alternative to the existing variable-rate VQ design algorithms for the applications of signal compression.