We study the gauged U ( 1 ) L μ - L τ scotogenic model with emphasis on latest measurement of LHCb R K ( ∗ ) anomaly and AMS-02 positron excess. In this model, neutrino masses are induced at one-loop level with Z 2 -odd particles, i.e., right-handed neutrinos N ℓ ( ℓ = e , μ , τ ) and inert scalar doublet η inside the loop. Meanwhile, the gauged U ( 1 ) L μ - L τ symmetry is broken spontaneously by the scalar singlet S , resulting to the massive gauge boson Z ′ . Provided certain couplings to quarks induced by heavy vector-like quarks, the gauge boson Z ′ would contribute to the transition b → s μ + μ - , hence explain the R K ( ∗ ) anomaly. As for the Majorana fermion DM N , the gauge boson Z ′ and the singlet Higgs H 0 will generate various annihilation channels, among which the N N → Z ′ Z ′ and N N → Z ′ H 0 ( → Z ′ Z ′ ) channel could be used to interpret the AMS-02 positron excess. We give a comprehensive analysis on model parameter space with consider various current constraints. The combined analysis shows that the R K ( ∗ ) anomaly and AMS-02 positron excess can be explained simultaneously.