Abstract: Recently, the extensive researches have done on percolation characteristics of different rules. Nevertheless, the impact of initial size distributions on percolation transition is rare in concern. In this paper, we investigate a modified ER (Eröds-Rényi) percolation process, in which the initial size distributions is set to exponential distribution. Through the analysis of Smoluchowski equation, it is found that although percolation transition is continuous compared to classical ER percolation process, the distributions of cluster size do not comply with the power-of distributions near the critical point, and both analytical and simulation results reveal that susceptibility does not satisfy the Curie-Weiss law.