In this paper, approximate calculation of channel log likelihood ratio (LLR) for wireless channels using Padé approximation is devised. Due to the lack of knowledge of the channel state information of a wireless fading channel, such as uncorrelated flat Rayleigh fading channels, calculation of exact LLR for these channels is quite complicated for a practical implementation. The previous work, LLR calculation using the Taylor approximation, quickly becomes inaccurate as the channel output leaves some derivative point. To overcome this problem, we devise a new LLR approximation using Padé approximation, which expresses the original function by rational form of two polynomials with the same total number of coefficients of the Taylor series, accelerates the Taylor approximation, is devised. By applying the proposed approximation to the iterative decoding and the low-density parity-check codes, we show the effectiveness of the proposed methods by simulation results and analysis based on the density evolution.