Flow around an inclined 5:2 prolate spheroid with the incidence angle alpha = 45 degrees is numerically investigated in a uniform shear flow. The Reynolds number based on the inflow center velocity U-c and the volume-equivalent sphere diameter D-e of the spheroid are considered at Re = 480, 600, 700, and 750. The non-dimensional shear rate K is ranged from 0 to 0.1. Five qualitatively different wake modes are observed, including a new mode characterized by multi-periodic shedding of hairpin vortices with regular rotation of the separation region. In general, the wake transition is suppressed with increasing shear rate. At high shear rates, the flow even reverts from unsteady to steady state at Re = 480, which we attributed to the reduction of the local Reynolds number at the leading-edge side of the spheroid. The time-averaged drag/lift coefficients and the Strouhal number increase with increasing the shear rate and the Reynolds number (except for K = 0). Finally, the effect of a sign-change of the incidence angle of the prolate spheroid on wake evolution is investigated. A physical exploration of the effect of the sign of the incidence angle and the amount of inlet shear is provided to give deeper insight into the physical mechanisms acting in the wake behind inclined non-axisymmetric bluff bodies in a shear flow. Published under an exclusive license by AIP Publishing.