In this article, a new kind of stationary zero-inflated Pegrams operator based integer-valued time series process of order p with Poisson marginal or ZIPPAR(p) is constructed for modelling a count time series consisting a large number of zeros compared to standard Poisson time series processes. Estimates of the model parameters are studied using three methods, namely Yule-Walker, conditional least squares and maximum likelihood estimation. Also h-step ahead coherent forecasting distributions of the proposed process for p = 1; 2 are derived. Real data set is used to examine and illustrate the proposed model with some simulation studies.