To mitigate damages due to natural disasters and abruptly changing weather, the importance of a weather radar network system (WRNS) is growing. Because radars in the current form of a WRNS operate in distinct frequency bands, operating a WRNS consisting of a large number of radars is very costly in terms of frequency resource. In this paper, we propose a novel WRNS in which multi-site weather radars share the same frequency band. By employing pulse compression with nearly orthogonal polyphase codes and sidelobe removal processing, a weather radar of the proposed frequency-sharing WRNS addresses inter-site and intra-site interferences simultaneously. Through computer simulations, we show the feasibility of the proposed system taking the performance requirement of a typical single weather radar into account