This paper presents, a new family of distributions, named the generalized linear failure rate family, generated from a generalized linear failure rate random variable is introduced. The new family contains five well-known families as special cases. Four particular distributions stemmed from the new family are explored. Mathematical properties of interest of the new family are derived. The maximum likelihood method is used to estimate the model parameters and its behavior is explored via detailed simulations. Finally, the importance of the new family is illustrated through two applications extracted from practice.