The key for Autonomous Underwater Vehicle (AUV) to implement target pursuit is to design high performance guidance law. The globose reference frame is adopted, and equations for 3-D relative motion between AUV and the target are built. Then the H∞ theory is used, and a new AUV nonlinear H∞ guidance law is obtained by solving Hamilton-Jacobi inequation. Simulation is taken on to verify the performance of H∞ guidance law. And the results show that the H∞ guidance law can help AUV overtake the target in less time, and the azimuth and pitching angle of the target line of sight are always staying at the initial numerical values. Furthermore, the normal load decreases to zero gradually. So the guidance law is effective for AUV to pursuit target.