We investigated Andreev reflection (AR) resonant tunneling through a precessing spin which is coupled to a normal metallic lead and a superconducting lead. The formula of the AR conductance at zero temperature is obtained as a function of chemical potential and azimuthal angle of the spin precessing by using the nonequilibrium Green function method. It is found that as the local spin precesses in a weak external magnetic field at Larmor frequency ω l , the AR tunneling conductance exhibits an oscillation at the frequency 2ω l alone. The amplitude of AR conductance oscillation enhances with spin-flip tunneling coupling increasing. The study also shows that spin-orbit interaction in tunneling barriers is crucial for the oscillations of AR conductance. The effect of local spin precessing and spin-flip tunneling coupling caused by spin-orbit interaction on the resonant behavior of the AR conductance is examined.