The k-modes algorithm was recently proposed to cluster mixed-type data. However, in solving clustering problems, the k-modes algorithm and its variants usually ask the user to provide the number of clusters in the data sets. Unfortunately, the number of clusters is generally unknown to the user. Therefore, clustering becomes a tedious task of trial-and-error and the clustering result is often poor, especially when the number of clusters is large and not easy to guess. Also, it is hard for a user to select the weight between categorical and numeric attributes in the k-modes algorithm. In this paper, a genetic algorithm for clustering large data sets with mixed-type data is proposed, and this algorithm can automatically search the number of clusters in the data set. Also, a weight can be automatically selected by the genetic algorithm to prevent favoring either type of attribute. Experimental results illustrate the effectiveness of the genetic algorithm.