We demonstrate microwave photonic radar with post-bandwidth synthesis, which can realize target detection with ultra-high range resolution using relatively small-bandwidth radio frequency (RF) frontends. In the proposed radar, two temporal-overlapped linear frequency-modulated (LFM) signals with the same chirp rate and different center frequencies are transmitted. By post-processing the de-chirped echoes in the receiver, a signal equivalent to that de-chirped from an LFM signal with the combined bandwidth is achieved. In a proof-of-concept experiment, two LFM signals with bandwidths of 8.4 GHz are exploited to achieve radar detection with an equivalent bandwidth of 16 GHz, and a range resolution of 1 cm is obtained.