The　management　of　computing　resources　through　the　computing　power　network　(CPN)　has　gradually　become　a　focal　point　of　research.　With　the　development　of　the　6th　generation　(6G)　mobile　networks,　some　promising　technologies　such　as　satellite-terrestrial　integrated　network　(STIN)　and　smart　endogenous　network　driven　by　artificial　intelligence　(AI)　are　increasingly　being　applied　in　Industrial　Internet　of　Things　(IIoT).　However,　several　issues　in　current　studies　are　worthy　of　attention:　1)　the　large　number　of　devices　powered　by　battery　in　IIoT,　2)　the　complex　communication　environments,　3)　the　finite　computing　resources　for　task　data　processing.　To　cope　with　these　challenges,　a　satellite-terrestrial　integrated　computing　power　network　(STICPN)　framework　is　introduced　in　this　article.　Within　this　framework,　a　task　offloading　link　selection　scheme　is　proposed,　which　minimizes　the　delay　and　the　consumption　of　energy.　The　task　offloading　optimization　problem　is　modeled　as　a　Markov　Decision　Process　(MDP).　Meanwhile,　deep　reinforcement　learning　(DRL)　algorithm　is　employed　to　adapt　to　the　dynamic　states　of　environment.　Specifically,　a　Dueling　Double　Deep　Q　Network　(D3QN)　is　used　to　make　optimal　decisions　and　delay　as　well　as　energy　consumption　can　be　reduced　significantly.　Moreover,　the　D3QN-based　scheme　extends　the　usage　time　of　IIoT　devices.　The　simulation　results　indicate　that　the　proposed　scheme　outperforms　the　comparison　schemes　significantly.　　©　2025　IEEE.