In this paper‎, ‎the analysis of count response with many zeros‎, ‎named as zero-inflated data‎, ‎is considered‎. ‎Assumes that responses follow a zero-inflated power series distribution‎. ‎Because of there is missing of the type of random in the covariate‎, ‎some of the data application‎, ‎various methods for estimating of parameters by using the score function with and without missing data for the proposed regression model are presented‎. ‎On the other hand‎, ‎known or unknown selection probability in the missing covariates results in presenting a semi-parametric method for estimating of parameters in the zero-inflated power series regression model‎. ‎To illustrate the proposed method‎, ‎simulation studies and a real example are applied‎. ‎Finally‎, ‎the performance of the semi-parametric method is compared with maximum likelihood‎, ‎complete-case and inverse probability weighted method‎.