Summary: In this paper, the maximum likelihood estimates (MLE’s) of the parameters of a finite mixture of modified Weibull (MW\((\alpha,\beta\gamma)\)) distributions are obtained based on type-I, type-II and progressively type-II censored samples. A simulation study is carried out to study the behavior of the mean squared errors. A real data set is introduced and analyzed using a mixture of two MW distributions and also using a mixture of two Weibull\((\alpha,\beta)\) distributions. A comparison is carried out between the mentioned mixtures based on the corresponding Kolmogorov-Smirnov (K-S) test statistic to emphasize that the MW mixture model fits the data better than the other mixture model.