The rationality and stability of mooring system are the key factors to ensure the reliability of buoy. We establish the catenary equation to deduce the calculation method of buoy chain length，give the critical value in the state of nature catenary，and analyze the anchoring stability by judging the state of the anchor system and calculating the anchoring force. Taking the setting of buoy in the Yangtze Estuary deepwater channel as an example，we analyze the stability of the mooring by this method，and propose the measures of increasing the mooring stability of buoy such as changing the mooring mode，reasonably configuring the chain length，and increasing the anchor force. The results can provide the references for the design of buoy.