This research proposes a new distribution for non-zero count data, namely the zero-truncated Poisson-weighted exponential distribution (ZTPWE). The Poisson- weighted exponential distribution(P-WE) has been proved to be a flexible two-parameter distribution; therefore, Zero-truncated models can be used to investigate data with- out zero counts. The combination of two such methods will be discussed in two parts. In the first part (the theoretical part), the probability mass function is derived from two methods. Then theoretical properties of the zero-truncated Poisson weighted exponential distribution are discussed: such as probability generating function, moment generating function, characteristic function, and moments. Furthermore, the method of maximum likelihood estimation is applied to estimate the parameters. In the second part, software simulations and fittings of two real data sets are discussed. The performance of the new model will be compared with other proposed zero-truncated models. i