With　the　large-scaled　data　generated　from　various　interconnected　machines　and　networks,　Industrial　Internet　of　Things　(IIoT)　provides　unprecedented　opportunities　for　facilitating　data　mining　for　industrial　applications.　The　current　IIoT　architecture　tends　to　adopt　cloud　computing　for　further　timely　mining　IIoT　data,　however,　the　openness　of　security-critical　IIoT　becomes　challenging　in　terms　of　unbearable　privacy　issues.　Most　existing　privacy-preserving　data　mining　(PPDM)　techniques　are　designed　to　resist　honest-but-curious　adversaries　(i.e.,　cloud　servers　and　data　users).　Due　to　the　complexity　and　openness　in　IIoT,　PPDM　is　significantly　difficult　with　the　presence　of　malicious　adversaries　in　IIoT　who　may　incur　incorrect　learned　models　and　inference　results.　To　solve　the　aforementioned　issues,　we　propose　a　framework　to　extend　existing　PPDM　to　guard　linear　regression　against　malicious　behaviors　(hereafter　referred　to　as　GuardLR).　To　prevent　dishonest　computations　of　cloud　servers　and　inconsistent　inputs　of　data　users,　we　first　design　a　privacy-preserving　verifiable　learning　scheme　for　linear　regression,　which　guarantees　the　correctness　of　learning.　In　this　article,　to　avoid　malicious　clouds　from　returning　incorrect　inference　results,　we　design　a　privacy-preserving　prediction　scheme　with　lightweight　verification.　Our　formal　security　analysis　shows　that　GuardLR　achieves　privacy,　completeness,　and　soundness.　Empirical　experiments　using　real-world　datasets　also　demonstrate　that　GuardLR　has　high　computational　efficiency　and　accuracy.　©　2021　IEEE.