We present a high-partial-wave (non-zero partial-wave) separable potential method (SPM) for investigating magnetically induced Feshbach resonances in collisions of ultracold atoms, then derive the Lippmann–Schwinger equation for two ultracold alkali-metal atoms in an external magnetic field and calculate the generalized scattering length and weakly bound state energy. We apply this method to the 6Li system and calculate the weakly bound state energy and the scattering volume near three typical p-wave Feshbach resonances. The calculated results by using the SPM agree well with those by using the coupled channel method and with experimental measurements. The SPM is expected to simplify computation of the three-body collision Faddeev equation in the vicinity of two-body high partial-wave Feshbach resonances.