In offline reinforcement learning (RL), one detrimental issue to policy learning is the error accumulation of deep \textit{Q} function in out-of-distribution (OOD) areas. Unfortunately, existing offline RL methods are often over-conservative, inevitably hurting generalization performance outside data distribution. In our study, one interesting observation is that deep \textit{Q} functions approximate well inside the convex hull of training data. Inspired by this, we propose a new method, \textit{DOGE (Distance-sensitive Offline RL with better GEneralization)}. DOGE marries dataset geometry with deep function approximators in offline RL, and enables exploitation in generalizable OOD areas rather than strictly constraining policy within data distribution. Specifically, DOGE trains a state-conditioned distance function that can be readily plugged into standard actor-critic methods as a policy constraint. Simple yet elegant, our algorithm enjoys better generalization compared to state-of-the-art methods on D4RL benchmarks. Theoretical analysis demonstrates the superiority of our approach to existing methods that are solely based on data distribution or support constraints.