Mean residual life is an important statistic in reliability analysis. Based on a general functional form of the derivative of the mean residual life, we propose a new lifetime distribution with an upside-down bathtub-shaped mean residual life function. The model has its mean residual life function in a simple, closed form so that further analysis based on the mean residual life can be easily carried out. We study the analysis and applications on both the mean residual life function, and the failure rate function of this model. Maximum likelihood method is used for parameter estimation. Numerical examples and comparisons indicate that the new model performs well in modeling lifetime data with bathtub-shaped failure rate functions, and upside-down bathtub-shaped mean residual life function.