In this paper we introduce a new lifetime distribution called type I half-logistic modified Weibull distribution. We investigate some mathematical properties including ordinary and conditional moments, Bonferroni and Lorenz curves, mean deviations and residual and reversed residual life functions. The maximum likelihood method is used to estimate the model parameters. We provide some simulation results to assess the performance of the proposed model. Two applications to real data sets show the flexibility of the new model compared with some nested and non-nested models.