The solid-state transmitters are widely adopted for weather radars, where pulse compression is operated to provide the required sensitivity and range resolution. Therefore, effective sidelobe suppression strategies must be employed, especially for weather observation. Currently, many methods can suppress the sidelobe to a very low level in the case of point targets or uniformly distributed targets. However, in strong convection weather process, the weather echo amplitude lies in a wide dynamic range and the main lobe of weak target is prone to being contaminated by the sidelobe of strong target, causing the degradation of weather fundamental data estimation, even generating artifacts and affecting the quantitative precipitation evaluation. In this paper, we propose a novel strategy which is the further processing of a general pulse compression radar to mitigate the effects of sidelobes. The proposed method is called the predominant component extraction (PCE), in which the re-weighting processing is operated after pulse compression, and then the echo of each bin is optimized and its energy will approach the real targets in each bin. It can improve the estimation of weak signals or even eliminate the artifact at the edge of the scene. Numerical simulation experiments and real-data verifications are implemented to validate the feasibility and superiority. It is noted that the proposed method has no requirement on the transmitted waveform and can be realized only by adding a step after pulse compression in the actual system.