Summary: This paper addresses the finite-time dynamic coverage problem for mobile sensor networks in unknown environments. By introducing a condition where dynamic coverage of all points within the sensing range of each sensor exceeds the desired coverage level by a positive constant, a switching control strategy is developed to guarantee the achievement of desired coverage of the whole mission domain in finite time. The environment is modeled by a density function and neural networks are introduced to learn the function. Due to the approximation capability of neural networks, the proposed control scheme can learn the environment without a priori knowledge on the structure of the density function.