Automotive radar pursues low cost and high performance, and especially hopes to improve the angular resolution under the condition of a limited number of multiple-input–multiple-output (MIMO) radar channels. Conventional time division multiplexing (TDM) MIMO technology has a limited ability to improve the angular resolution without increasing the number of channels. In this paper, a random time division multiplexing MIMO radar is proposed. First, the non-uniform linear array (NULA) and random time division transmission mechanism are combined in the MIMO system, and then a three-order sparse receiving tensor of a range-virtual aperture-pulse sequence is obtained during echo receiving. Next, this sparse three-order receiving tensor is recovered by using tensor completion technology. Finally, the range, velocity and angle measurements are completed for the recovered three-order receiving tensor signals. The effectiveness of this method is verified via simulations.