Radar has been widely used for military, security, and rescue purposes, and modern radar should be reconfigurable at multi-bands and have programmable central frequencies and considerable bandwidth agility. Microwave photonics or photonics-assisted radio-frequency technology is a unique solution to providing such capabilities. Here, we demonstrate an all-optical central-frequency-programmable and bandwidth-tailorable radar architecture that provides a coherent system and utilizes one mode-locked laser for both signal generation and reception. Heterodyning of two individually filtered optical pulses that are pre-chirped via wavelength-to-time mapping generates a wideband linearly chirped radar signal. The working bands can be flexibly tailored with the desired bandwidth at a user-preferred carrier frequency. Radar echoes are first modulated onto the pre-chirped optical pulse, which is also used for signal generation, and then stretched in time or compressed in frequency several fold based on the time-stretch principle. Thus, digitization is facilitated without loss of detection ability. We believe that our results demonstrate an innovative radar architecture with an ultra-high-range resolution.