In this paper, a frequency-wavenumber decoupling algorithm with high-efficiency and high-precise for three-dimensional (3-D) multiple-input-multiple-output synthetic aperture radar (MIMO-SAR) imaging is proposed. Based on one-dimensional (1-D) MIMO array combined with synthetic aperture scan along another dimension, MIMO-SAR imaging scheme allows the number of array elements to be greatly reduced compared with the two-dimensional (2-D) MIMO arrays. By multi-dimensional Fourier transforming and Method of Stationary Phase (MSP), analytical expression of the object function in the frequency-wavenumber domain was derived. By further expanding the range Fourier transform factor to its Taylor series form, the range compression can be realized by a simple fast Fourier transform (FFT) without multi-dimensional interpolation. After that, a decoupling factor was multiplied to compensate for the cross-range and range coupling in frequency domain. Finally, 2-D IFFT is carried out after rearrangement in the MIMO spatial frequency to get a fully focused 3-D image. Simulation and experimental results demonstrated that the algorithm can obtain the same high-precision images as back projection (BP) algorithm, and has the same high efficiency as range migration algorithm (RMA) while avoiding cumbersome multi-dimensional interpolation. A bistatic prototype imaging system in 0.1 THz band was designed for the proof-of-principle experiments. The 3-D reconstruction results of different targets were presented to verify the theoretical results and effectiveness of the proposed algorithm for MIMO-SAR imaging.