An analytical method for approximate performance evaluation of binary linear block codes using an additive white Gaussian noise channel model with binary phase-shift keying modulation is presented. We focus on the probability density function of the bit log-likelihood ratio (LLR), which is expressed in terms of the Gram-Charlier series expansion. This expansion requires knowledge of the statistical moments of the bit LLR. We introduce an analytical method for calculating these moments. This is based on some recursive calculations involving certain weight enumerating functions of the code. It is proved that the approximation can be as accurate as desired, if we use enough terms in the Gram-Charlier series expansion. Numerical results are provided for some examples, which demonstrate close agreement with simulation results.