A Frequency Diverse Array (FDA) radar achieves the uniform coverage of a large-scale airspace within a pulse duration by introducing a designed carrier frequency increment between adjacent transmitting elements. Unfortunately, the beam scanning property of an FDA radar leads to a reduction in dwell time at certain azimuth direction, which results in the deterioration of the range resolution. To solve this problem, we propose a novel coherent FDA radar waveform in the space–time domain, in which spatial phase encoding is introduced between transmitting elements to significantly improve the range resolution of a coherent FDA radar. A nonlinear frequency modulation signal is also used in the time domain to obtain a low-range Peak to SideLobe Ratio (PSLR). Simulation results verify that the proposed FDA radar waveform design realizes both a low PSLR and high range resolution. Finally, we analyze the Doppler sensitivity of our proposed method for the observation of high-speed moving targets.