We introduce Wave-CAIPI acquisition-reconstruction technique to accelerate 3D MR Imaging by an order of magnitude, with negligible noise amplification and image artifact penalties. Wave-CAIPI involves playing sinusoidal Gy and Gz gradients during the readout of each phase encoding line while modifying the phase encoding strategy to incur slice shifts as in 2D-CAIPI. This combination spreads out aliasing due to data undersampling evenly in all spatial directions, thereby taking full advantage of 3D coil sensitivity distribution of the receiver coil. By expressing the voxel spreading effect as a convolution in image space, an efficient reconstruction scheme that recovers the undersampled data without data gridding is proposed. Wave-CAIPI enables full-brain gradient echo (GRE) acquisition in 2.3 minutes with 1 mm isotropic voxel size and R=3×3 acceleration, and yields maximum g-factors (noise amplification) of 1.08 at 3T, and 1.05 at 7T. Relative to state of the art accelerated imaging methods, this is a factor of 2 reduction in maximum g-factor at 3T and 7T.