Frequency diverse array (FDA)-multiple-input multiple-output (MIMO) radars can generate a range-angle two-dimensional transmit steering vector (SV), which is capable of suppressing mainbeam deceptive jamming in the transmit–receive frequency domain by utilizing additional degrees of freedom (DOFs) in the range dimension. However, when there are target SV mismatch, covariance matrix estimation error and target contamination, the jamming suppression performance degrades severely. In this paper, a robust adaptive beamforming algorithm for anti-jammer application based on covariance matrix reconstruction is proposed in FDA-MIMO radar. In this method, the residual noise is further determined by using the spatial power spectrum estimation approach, which results in improved estimation accuracy of the signal covariance matrix and the desired target SV. The jamming SV is obtained from vectors in the intersection of two subspaces (namely, the signal-jamming subspace derived from the sample covariance matrix (SCM) and the jamming subspace generated from the jamming covariance matrix) by an alternating projection algorithm. Furthermore, the jamming power is obtained by exploiting the orthogonality between the different SVs. With the obtained parameters of target and jamming, the optimal adaptive beamformer weight vector is calculated. Simulation results demonstrate that the proposed algorithm can cope with the mainbeam deceptive jamming suppression under various model mismatches and has excellent performance over a wide range of signal-to-noise ratios (SNRs).