Computing quantum capacity of Gaussian channels is an interesting problem because of its various applications. Single-mode phase-insensitive Gaussian channels, including thermal channels are most simple but an important class of Gaussian channels. However there is still large gap between lower and upper bound, and also we don't even know the one-shot capacity of thermal channels. In this talk, I'll present various methods to obtain upper bounds, and its application by introducing achievable rate using GKP code.