This paper presents a method of using Gaussian process regression to model spatial functions for mobile wireless sensor networks. A distributed Gaussian process regression (DGPR) approach is developed by using a sparse Gaussian process regression method and a compactly supported covariance function. The resultant formulation of the DGPR approach only requires neighbor-to-neighbor communication, which enables each sensor node within a network to produce the regression result independently. The collective motion control is implemented by using a locational optimization algorithm, which utilizes the information entropy from the DGPR result. The collective mobility of sensor networks plus the online learning capability of the DGPR approach also enables the mobile sensor network to adapt to spatiotemporal functions. Simulation results are provided to show the performance of the proposed approach in modeling stationary spatial functions and spatiotemporal functions.