Until now, many studies related circular data are carried out, but the focuses are mainly on mildly peaked symmetric or asymmetric cases. In this paper we studied a modeling process for sharply peaked asymmetric circular data. By using wrapped Laplace, which was firstly introduced by Jammalamadaka and Kozbowski (2003), and its mixture distributions, we considered the model fitting problem of multi-modal circular data as well as unimodal one. In particular we suggested EM algorithm to find ML estimates of the mixture of wrapped Laplace distributions. Simulation results showed that the suggested EM algorithm is very accurate and useful.