The output signal-to-clutter-plus-noise ratio (SCNR) of space-time adaptive processing (STAP) decreases due to the dispersion of the transmit energy for traditional airborne multiple-input-multiple-output (MIMO) radar. Moreover the sufficient training samples cannot be provided to estimate the clutter covariance matrix (CCM) in the non-stationary environment. To solve these problems, a novel STAP method based on the atomic norm minimization (ANM) for transmit beamspace-based (TB-based) airborne MIMO radar is proposed. Firstly, the signal model of TB-based MIMO-STAP is established, then the optimizing principle based on the ANM is presented to design TB matrix used to focus the transmit energy in a certain spatial sector. Moreover, the beampattern corresponding to the TB matrix is close to the desired beampattern in different working modes. Meanwhile, to further reduce the number of the training samples, an accurate CCM estimation with the low-rank property is yielded by applying the ANM theory into the TB-based MIMO-STAP. Compared with the conventional MIMO-STAP with the orthogonal waveforms, simulation results show that the output SCNR of TB-based MIMO-STAP is improved. Moreover, since the CCM of the proposed method is estimated in continuous domain, the off-grid problem can be avoided. Thus, the clutter suppression performance is superior over the conventional sparse representation based STAP (SR-STAP). Meanwhile, simulation results show that the performance of the proposed method is close to that of the statistical classical MIMO-STAP and outperforms that of SR-STAP. Furthermore, it can be shown from the simulation results that the clutter suppression performance is still robust when the low-rank property of the CCM is destroyed.