‎Abstract: In this paper, a new mixture modelling using the normal mean-variance mixture of Lindley (NMVL) distribution has been considered. The proposed model is heavy-tailed and multimodal and can be used in dealing with asymmetric data in various theoretic and applied problems. We present a feasible computationally analytical EM algorithm for computing the maximum likelihood estimates. The behavior of the obtained maximum likelihood estimators is studied with respect to bias and mean squared errors through conducting a simulation study. Two examples with flow cytometry data are used to illustrate the applicability of the proposed model.