We present an efficient algorithm for computing the heat capacity of a large-scale molecular system. The new algorithm is based on a special Gaussian quadrature whose abscissas and weights are obtained by a simple Lanczos iteration. Our numerical results have indicated that this new computational scheme is quite accurate. We have also shown that this method is at least a hundred times faster than the earlier apporach that is based on esitimating the density of states and integrating with a simple quadrature formula.