We study the competition between the p-wave and the p+ip superfluid solutions in a holographic model with applied magnetic field intensity H. We find that when H is turned on, both the grand potential and the critical temperature of the p+ip solution are shifted, while the p-wave solution is only slightly affected. Combining the effect of H and back reaction parameter b, we build H − T phase diagrams with a slit region of p+ip phase. The zero (or finite) value of H at the starting point of the slit region is related to second (or first) order of the p-wave phase transition at zero magnetic intensity, which should be universal in systems with degenerate critical points (spinodal points) at zero magnetic field.