The high proportion of renewable energy integration and the dynamic changes in grid topology necessitate the enhancement of voltage/var control (VVC) to manage voltage fluctuations more rapidly. Traditional model-based control algorithms are becoming increasingly incompetent for VVC due to their high model dependence and slow online computation speed. To alleviate these issues, this paper introduces a graph attention network (GAT) based deep reinforcement learning for VVC of topologically variable power system. Firstly, combining the physical information of the actual power grid, a physics-informed GAT is proposed and embedded into the proximal policy optimization (PPO) algorithm. The GAT-PPO algorithm can capture topological and spatial correlations among the node features to tackle topology changes. To address the slow training, the ReliefF-S algorithm identifies critical state variables, significantly reducing the dimensionality of state space. Then, the training samples retained in the experience buffer are designed to mitigate the sparse reward issue. Finally, the validation on the modified IEEE 39-bus system and an actual power grid demonstrates superior performance of the proposed algorithm compared with state-of-the-art algorithms, including PPO algorithm and twin delayed deep deterministic policy gradient (TD3) algorithm. The proposed algorithm exhibits enhanced convergence during training, faster solution speed, and improved VVC performance, even in scenarios involving grid topology changes and increased renewable energy integration. Meanwhile, in the adopted cases, the network loss is reduced by 6.9%, 10.8%, and 7.7%, respectively, demonstrating favorable economic outcomes.