Wireless rechargeable sensor networks have been applied to all aspects of the real world today. Though sensors can collect energy from the environment, the energy collection cannot support sensors to work continuously as usual. Energy scheduling problems have to be solved. In this paper, we study the energy allocation problem of a rechargeable sensor network that can monitor multiple random events. It is assumed that each event follows a Poisson process, the energy received by the sensor is random, and each sensor has a chance to be assigned to detect one or more events. In the paper, we also introduce multi-objective nonlinear programming to solve the problems of nonlinearity and energy. Two algorithms are also proposed to obtain the programming’s Pareto optimal solution. At last, we conduct a number of practical simulations to verify our results.