A weather radar extracts the weather information from the return echoes which consist of scattered electromagnetic wave signals from rain, cloud and dust particles, etc. The characteristics of Doppler weather signal and ground clutter should be analyzed to extract the accurate weather information. However, the conventional symmetric weather Doppler model is somewhat inappropriate in representing various weather situations. Therefore, the improved model is suggested to describe the skewness in the Doppler spectrum model. Using the suggested model, many various weather signals can be simulated efficiently in time and spectral domain according to weather situations, operation environment and system characteristics. This simulation method may be very helpful in verifying the accuracy of the weather information extraction algorithms and developing the new system for further performance improvement.