The　rapid　development　of　Industrial　IoT　(IIoT)　opens　up　promising　possibilities　for　data　analysis　and　machine　learning　in　IIoT　networks.　As　a　distributed　paradigm,　federated　learning　(FL)　allows　numerous　IIoT　devices　to　collaboratively　train　a　global　model　without　collecting　their　local　data　together　in　central　servers.　Unfortunately,　a　centralized　server　used　to　aggregate　local　gradients　can　be　compromised　and　forge　the　result,　which　incurs　the　need　for　aggregation　verification.　Several　approaches　focusing　on　verifying　the　correctness　of　aggregation　have　been　proposed.　However,　it　is　still　an　open　problem　since　devices　have　to　devote　more　computation　resources　for　verification,　which　are　especially　not　friendly　to　resource-constrained　IIoT　devices.　Furthermore,　verifying　weighted　aggregation　has　not　been　supported　in　existing　approaches.　In　this　paper,　we　propose　an　efficient　verifiable　federated　learning　approach　for　IIoT　networks,　which　verifies　the　aggregation　of　gradients　and　requires　lowest　burden　on　IIoT　devices　by　introducing　zero-knowledge　proof　techniques.　Moreover,　our　design　supports　weighted　aggregation　verification　to　validate　the　aggregation　of　weighted　gradients　in　the　cloud　server.　By　comparing　the　proposed　approach　with　the　state-of-the-art　schemes　including　VerifyNet　and　VeriFL,　we　demonstrate　the　superior　performance　of　our　approach　for　resource-constrained　devices,　which　minimizes　the　computational　overheads　of　the　IIoT　devices.