A modified FDM/TDM method was first used by Sato to study the achievable rate region of degraded Gaussian interference channel. Recently Sason used this method to get an achievable rate region of Gaussian interference channel. In this paper, we generalize this method in terms of the transmission mode and frequency band allocation, and obtain an achievable rate region for Gaussian interference channel, which improves the existing computable rate regions for both the weak and moderate interferences. We note that this modified FDM/TDM is different to time sharing and the difference depends on the activeness and concavity of the constraints. The achievable sum rate of symmetric Gaussian interference channel is derived for a subregion of the classical Han-Kobayashi region, and subsequently, for the proposed new achievable rate region.