Kumar and Shibu proposed a modified version of intervened Poisson distribution (IPD), namely the modified intervened Poisson distribution (MIPD) for tackling situations of further interventions useful for certain practical problems. Here we consider some finite mixtures of MIPD and study some of its important properties. The identifiability condition of the mixture distribution is derived and the parameters of the mixture model are estimated by various methods such as method of factorial moments and method of maximum likelihood. In addition, this mixture model is fitted to some real life data sets.