Recently Underwater Wireless Sensor Networks have rapidly developed and been widely adopted to meet all kinds of applications, while they are exposed to an open underwater environment which is particularly vulnerable to various attacks, among which Sybil attack is one of the most common and harmful one. In this case, it is urgent to find an effective method to detect the Sybil attack. Our paper puts forward a novel scheme based on state information of nodes to detect the Sybil attack. We implement the feature of our scheme through both by numerical analysis and simulation performance in MATLAB. And the simulation results demonstrate that the detecting accuracy can be up to 94 percent. Our proposed scheme can efficiently detect the Sybil nodes.