© 2018 IEEE. The Non-homogeneous Poisson process is a point process with time-varying intensity across its domain, the use of which arises in numerous areas in signal processing and machine learning. However, applications are largely limited by the intractable likelihood function and the high computational cost of existing inference schemes. We present a sequential inference framework that utilises generative Poisson data and sequential Markov Chain Monte Carlo (SMCMC) algorithm to enable online inference in various applications. The proposed model is compared to competing methods on synthetic datasets and tested with real-world financial data.