Abstract: In environmental monitoring applications, there are often various objects to be monitored by sensor networks. In this scenario, each heterogeneous node carries some different sensors, and the coverage of multiple areas is required in order to monitor every different subobject. In sensor networks with random distributed nodes, an average subnet lifetime model is proposed to evaluate the average lifetime of nodes sensing one subobject. Given the constraints of cost budget and area coverage of different objects, a multi-objective multi-coverage algorithm based on integer vector programming is proposed to balance the cost and coverage performance, as well as the monitoring life of different subobjects. The algorithm is divided into two steps. The first step is to compute the number of each type of sensors used to monitor one subobject, and the second step is to determine the number of different kinds of heterogeneous nodes based on the average subnet life model. To solve the proposed vector programming issues, two suboptimal methods are given. In the simulation experiments, different suboptimal methods are compared, and the computational complexity of the proposed algorithm is analysed. Simulation examples verify the effectiveness of the proposed algorithm in the multi-objects monitoring applications.