An　efficient　method　is　proposed　to　deal　with　high-dimensional　reliability　problems.　The　critical　contribution　lies　in　developing　an　advanced　DGPR　model,　which　effectively　combines　deep　neural　network　(DNN)-based　dimension　reduction　and　Gaussian　process　regression　(GPR)　model.　Specifically,　the　parameters　of　both　the　DNN　and　the　GPR　are　calibrated　through　a　joint-training　scheme,　and　the　network　architecture　of　the　DGPR　is　optimally　selected　via　a　grid-search　scheme　coupled　with　five-fold　cross　validation.　In　this　regard,　both　the　supervised　extraction　of　low-dimensional　latent　space　and　the　training　of　GPR　in　the　latent　space　are　intrinsically　achieved　by　the　DGPR.　Then,　an　active　learning　strategy　is　adopted　to　combine　the　DGPR　and　the　subset　simulation　for　reliability　analysis.　To　verify　the　efficacy　of　the　proposed　approach,　three　numerical　examples　are　investigated　and　comparisons　are　made　against　other　reliability　methods.　Numerical　results　demonstrate　that　the　proposed　approach　gains　reasonable　computational　cost　savings　whilst　maintaining　satisfactory　accuracy　of　reliability　results.