Different from traditional multiple-input and multiple-output (MIMO) radar, the frequency diverse array MIMO (FDA-MIMO) radar generates beampattern that is dependent on both range and angle, making it applicable for joint range–angle estimation of targets. In this paper, we propose a novel time reversal based FDA-MIMO (TR-FDA-MIMO) approach for target detection. Based on the time reversal theory, the TR-FDA-MIMO signal model is established, the TR transmitting–receiving and signal processing procedure are analyzed, and the resulting range–angle spectra for targets imaging are acquired by utilizing the multiple signal classification algorithm. Numerical simulations are carried out for both single and multiple targets cases. The imaging resolution and robustness to the noise of the proposed approach are investigated and results are compared with conventional FDA-MIMO radar. It turned out that by cooperating with TR, the performance of FDA-MIMO radar for target range–angle estimation is effectively enhanced, consequently improving its applicability in practical target-detecting cases.