Extreme rainfall events due to heavy rainfall can vary greatly. This variability can be explained by different factors such as season of the year, temperature and local topography, among others. Statistical models using Extreme Value Theory have been used to model extreme weather events which assume stationarity of rainfall process. However, the stationarity requirement is not met in reality for rainfall data because rainfall time series usually exhibit seasonality. A stochastic model based on a non-homogeneous Poisson Process (NHPP) charactezised by a time-dependent intensity of rainfall occurrence, is employed in to study the seasonal and trend effects on extreme events modelling of daily rainfalls exceeding prefixed threshold value. Dataset from 14 Tanzania rainfall stations over the period 1981–2014 was used. The Akaike information criterion and likelihood ratio test methods were used to select NHPP model that best fits the data. The results showed a good fit for time–varying intensity of rainfall occurrence process by the first order harmonic Fourier law and improved analysis as well as modelling of extreme rainfall using NHPP intensity function.