In this letter, a transmit waveform covariance matrix design method based on the first null constraint is proposed for the transmit beampattern design of Multiple-Input Multiple-Output radar. This method effectively concentrates more transmit energy within the beam, thereby enhancing the detection capability of radar. Additionally, considering the presence of steering vector errors in the radar transmit array, a robust waveform design method under the same constraint is also proposed. Finally, simulation experiments demonstrate the effectiveness of the proposed method.