A frequency diverse array (FDA) radar has attracted wide attention, due to its capability to provide a range-angle dependent beampattern and to scan the spatial without phase shifters or rotating arrays. However, FDA systems will suffer from low echo signal energy or high sidelobe peaks when detecting targets by beamforming based on existing receivers. To reduce the sidelobe peak of detection results while increasing the echo signal energy, in this paper, we propose an FDA radar system based on diversity linear frequency modulation waveforms. Correspondingly, we propose a receiver architecture with a time-variant beamforming chain. The proposed system retains the ability of the FDA system to automatically spatial beam scanning, owing to the frequency increment across elements. By increasing the pulse duration of transmitted signals, we enhance the echo signal energy. By applying the artificial bee colony algorithm to design the bandwidth of each chirp signal, the proposed system reduces the sidelobe level of detection results while increasing pulse width. Numerical simulation results are presented to demonstrate the effectiveness of the proposed system.