In this paper we propose a new importance sampling (IS) scheme to estimate the low error-rate performance of LDPC codes over a Rayleigh fading channel. It biases the Rayleigh fading distribution as well as the noise distribution in order to improve the quality of estimation. The proposed IS scheme is compared with the Monte-Carlo (MC) simulator and other IS schemes in terms of its efficiency and accuracy. Numerical results show that the proposed IS estimator is much more efficient than the MC estimator and other IS estimators from the viewpoint of the required simulation time. Furthermore, the proposed IS scheme provides a more accurate performance estimation of LDPC codes over a Rayleigh fading channel with only a limited simulation time than other IS schemes.