Influence maximization which asks for $k$-size seed set from a social network such that maximizing the influence over all other users (called influence spread) has widely attracted attention due to its significant applications in viral marketing and rumor control. In real world scenarios, people are interested in the most influential users in particular topics, and want to subscribe the topics-of-interests over social networks. In this paper, we formulate the problem of influential users subscription on time-decaying social stream, which asks for maintaining the $k$-size influential users sets for each topic-aware subscription queries. We first analyze the widely adopted sliding window model and propose a newly time-decaying influence model to overcome the shortages when calculating the influence over social stream. Developed from sieve based streaming algorithm, we propose an efficient algorithm to support the calculation of time-decaying influence over dynamically updating social networks. Using information among subscriptions, we then construct the Prefix Tree Structure to allow us minimizing the times of calculating influence of each update and easily maintained. Pruning techniques are also applied to the Prefix Tree to optimize the performance of social stream update. Our approach ensures a $\frac{1}{2}-ε$ approximation ratio. Experimental results show that our approach significantly outperforms the baseline approaches in efficiency and result quality.