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This study introduces a two-parameter model called a new Weibull inverted exponential (AWIE) distribution for modeling lifetime datasets. The proposed model uses the new Weibull-X characterizations. The density of the proposed model can be symmetrical, left skewed, reverse J-shaped, unimodal and increasing, and bathtub shaped failure rate. Some mathematical properties of the proposed distribution are investigated. The two parameters of the proposed model are obtained by maximum likelihood. The regression and Bayesian models of the proposed model are obtained in a class form. Two real-life data sets are used to illustrate the applicability of the proposed model. The results of the test statistics show that the proposed new model gives a better fit compared to some related distributions in literature.