Airy beam light-sheet microscopy (LSM) has a very wide field-of-view and generates a high contrast image, which is a big advantage for large cubic sample imaging. Due to the effect of side lobes of Airy beam, shadow artifacts are incurred and therefore, proper image deconvolution is required to reconstruct the real image from the measured image. In this Letter, we propose a block-by-block reconstruction approach based on a 3D deconvolution algorithm, the Richardson-Lucy algorithm with roughness regularization, for Airy beam light-sheet microscopy (ALSM). The simulation and experimental results show that the proposed 3D deconvolution approach significantly outperforms the existing 1D deconvolution technique in restored image-quality, which makes it very promising for large field-of-view (FOV) ALSM image reconstruction.