The connectivity is one of the fundamental properties for wireless sensor networks (WSNs). However, because of the presence of Rayleigh fading channel and other unstable factors, it is difficult to study the wireless sensor network being connected. In this paper, we present a new approximate expression for lower bound of the conditional probability of the network being connected and obtain the whole network connectivity under Rayleigh fading channel. Further, the analytical results are obtained and simulation shows that the two proposed lower bounds of the conditional probability on the whole network connectivity under Rayleigh fading channel have similar results. Besides, the connectivity probability of the wireless sensor network is considerably decreased under the Rayleigh fading channel.