This paper addresses the system lifetime maximization algorithm in multi-hop sensor network system. A multi-hop sensor network consists of many battery-driven sensor nodes that collaborate with each other to gather, process, and communicate information using wireless communications. As sensor-driven applications become increasingly integrated into our lives, we propose a energy-aware scheme where each sensor node transmits informative data with adaptive data rate to minimize system energy consumption. We show the optimal data rate to maximize the system lifetime in terms of remaining system energy. Furthermore, the proposed algorithm experimentally shows longer system lifetime in comparison with greedy algorithm.