The problem of large-scale spatial multiple testing is often encountered in various scientific research fields, where the signals are usually enriched on some regions while sparse on others. To integrate spatial structure information from nearby locations, we propose a novel approach, called {\bf STR}ucture-{\bf A}daptive {\bf W}eighting (STRAW) procedure, for large-scale spatial multiple testing. The STRAW procedure is capable of handling a broad range of spatial settings by leveraging a class of weighted p-values and is fully data-driven. Theoretical results show that the proposed method controls the false discovery rate (FDR) at the pre-specified level under some mild conditions. In practice, the local sparsity level, defined as the probability of the null hypothesis being not true, is commonly unknown. To address this issue, we develop a new method for estimating the local sparsity level by employing the kernel-smooth local false discovery rate (Lfdr) statistic. The superior numerical performance of the STRAW procedure is demonstrated by performing extensive simulation studies and a real data analysis.