This article presents a kriged compressive sensing (KCS) approach to reconstruct acoustic fields using measurements collected by underwater mobile sensing platforms. The KCS approach has two steps. First, initial estimates are obtained from a kriging method by leveraging spatial statistical correlation properties of the acoustic fields. Second, selected initial estimates, treated as virtual samples, are combined with the measurements to perform field reconstruction through compressive sensing. To differentiate the fidelity between real measurements and virtual samples, we use the kriging variance to determine weight coefficients for the virtual samples estimated from kriging. Simulation results show that the proposed KCS approach can improve the reconstruction performance, in terms of the peak signal-to-noise ratio and structural similarity metrics. The KCS performance has been validated based on the acoustic intensity measurements collected by an autonomous underwater vehicle in a lake. The KCS methods have also been applied to process the ambient sound level measurements collected by an underwater glider in the South China Sea. The proposed KCS method leads to better performance than either the compressive sensing or the kriging method alone.