Vector quantization with an optimal codebook is attractive for lossy data compression. So far, a number of codebook design algorithms have been proposed to minimize the mean square error, MSE. However, these algorithms have a problem that MSE minimization sometimes causes an unacceptable maximum-distortion, which is very important in several applications. This paper proposes a competitive learning algorithm with controlling maximum distortion that designs a codebook giving a maximum distortion within a given error bound. The proposed algorithm assigns a code vector to an input vector with a too large distortion. Experimental results showed that the algorithm has both maximum-distortion control and MSE minimization capability.