In this paper, we introduce the Topp-Leone generalized exponential power series class of distributions. It is obtained by compounding the Topp-Leone generalized exponential distribution and the power series family. This new class of distributions can be applied in reliability of parallel system with identical components, where lifetime of each component has the Topp-Leone generalized exponential distribution. The proposed distribution contains several lifetime models such as the Topp-Leone generalized exponential-geometric, Topp-Leone generalized exponential-binomial,Topp-Leone generalized exponential-poisson, and Topp-Leone generalized exponential-logarithmic distributions as special cases. The hazard function of the new distributions can be increasing, decreasing, and v shaped. We obtain several properties of this distributions such as probability density function, quantile and moments. The parameter estimation using maximum likelihood estimation is discussed. Some real datasets are illustrated the flexibility and potentiality of the Topp-Leone generalized exponential power series class of distributions.