We consider the secure transmission of information over Rayleigh fading wiretap channel when the main and eavesdropper channels are correlated there. Assuming that before transmission the transmitter knows the full channel state information (CSI) of both the main and eavesdropper channels, we analyze the average secrecy capacity with limited signal-to-noise ratio (SNR), for which a simple closed-form expression is derived based on the typical Marcum Q function. This is achieved by exploring the symmetry property between the main channel and eavesdropper channel to avoid a complicated integration involved in the secrecy capacity analysis, such that the secrecy capacity derivation can be significantly simplified. Numerical results are also provided to confirm our analytical ones.