Summary: The Fréchet probability distribution is the power transformation of an exponentially distributed variable and is widely applied for problems in engineering. The Lomax (Pareto II) probability distribution has wide application in a variety of fields. In this paper, we introduce a new statistical distribution constructed by composition of the cumulative density functions (cdf) of Fréchet probability distribution and Lomax probability distribution and is named as the Lomax-Fréchet distribution. It may have wider applicability in engineering, order statistics and other fields as it has more number of parameters. We derive expressions for its moments, characteristic function, hazard rate function and survivor function. We plot some graphs for its probability density function (pdf) using the software {Mathematica}. We also investigate the variation of the skewness and kurtosis and discuss estimation by the method of maximum-likelihood.