In this paper a genetic algorithm for clustering is proposed. The algorithm is based on the variable length chromosomes and the notion of local points density in the clustered set. Its role is to identify the number of clusters in the clustered set and to partition this set into particular clusters. The tests were conducted for two different sets of two dimensional data. The algorithm performed well in both cases. The tests presented the ability of the algorithm to partition the subsets combined with the thin dense area into separate clusters.