Sensing coverage is a fundamental issue for many applications in wireless sensor networks. Due to sensors resource limitations, inherent uncertainties associated with their measurements, and the harsh and dynamic environment in which they are deployed, having a QoS-aware coverage scheme is a must. In this paper, we propose a Trust-based Probabilistic Coverage algorithm, which leverages the trust concept to tackle the uncertainties introduced by the nodes and the environment, in which they operate. We formulate this problem as an Integer Linear Programming (ILP) problem, which is able to always guarantee the required QoS despite uncertainties introduced by node and/or environment. In consideration of the limitation of ILP, we also put forward a greedy heuristic algorithm to achieve almost the same ILP results without suffering from complexities imposed by ILP. We examine our heuristic with different input parameters and compare it with the ILP approach. Simulation results are presented to verify our approaches.