A weather radar usually extracts the necessary information from the return Doppler spectrum moment estimates. Phase stability is a very important factor in obtaining accurate and reliable information in a Doppler weather radar system since the system phase noise may seriously degrade the weather spectrum moment estimation quality. These spectrum moment estimates are commonly obtained using the pulse pair method which is simple to implement and fast enough to process an enormous amount of weather radar data in real time. Therefore, an analytical method is developed in this paper to analyze and quantify the phase noise effects on the pulse pair spectrum moment estimates in terms of the phase noise power and broadness.