For a sound field observed on a planar sensor array, compressive sensing (CS) reconstructs the two-dimensional (2D) direction-of-arrival (DOA) of multiple sources using a sparsity constraint. Conventional compressive beamforming methods suffer from grid mismatch, where true DOAs do not fall on the discretized angular search grid. This paper adopts a CS-based model, which can reconstruct block-sparse signals, and the model treats DOAs and the off-grid DOA compensation parts as blocks to deal with the off-grid 2D beamforming. The method is illustrated by numerical simulations and shows high estimation accuracy. Also, the approach does not require a specific array configuration and is suitable for arbitrary planar array geometry, which is practically useful. Since propeller tip vortex cavitation induces noise sources located sparsely near the propeller tip, the high-resolution of the method is demonstrated with experimental data from cavitation tunnel experiments.