Experimentally, black phosphorus (BP) displays a promising electrochemical performance as an anode for both Li ion and Na ion batteries. The feature of fast charge-discharge capability is very desirable for an anode material. We investigated the intercalation mechanism of a single Na and Li and the diffusion mechanism in BP by means of first-principles simulation. We found that a large tunnel forms because of the sliding of phosphorus interlayers with a single Na and Li intercalation and that the Na and Li diffusion within the tunnel along the a axis is very fast. This makes BP a competitive and promising anode for both Na ion and Li ion batteries. The different behaviors of Na and Li in BP are also discussed.