Due to the contradiction between the high sensitivity requirement and low transmission power of weather radars with solid-state transmitters, a pulse compression technique is necessary. For the purpose of range sidelobe suppression, methods based on amplitude modulation and a mismatched filter are commonly used for target detection radars, which are not applicable for weather observations because of its drawbacks such as main lobe expansion and power loss. This letter presents a nonlinear frequency modulation pulse compression waveform to achieve a very low range sidelobe level. A mathematical model for waveform design is established, in which the time-frequency relation is expressed as the combination of a linear function and a sine series. Thus, a set of parameters can fully characterize the time-frequency curve. By using a simulated annealing algorithm, the optimal parameter set can be obtained, which shows that a peak sidelobe level under -60 dB is achievable. Finally, this kind of waveform is implemented on hardware, and its performance is verified.