The invention provides an AUV (autonomous underwater vehicle) three-dimension curve path tracking control method based on iteration. The method comprises the following steps that 1, initialization is carried out; 2, the relative tracking error of the current AUV position and the virtual guide point on an expected path in an AUV carrier coordinate system at the initial moment is calculated; 3, the expected moving speed of the virtual guide point on the expected path and the AUV kinematics tracking control law are calculated; 4, the iteration is adopted on the basis of the kinematics equivalent control law, and the kinematics equivalent control law of the underactuated AUV three-dimension path tracking is deduced; and 5, the distance between the current AUV position Eta<n>=(x, y, z) and the demarcated steering point WPk=(xk, yk, zk) is calculated, when the distance is smaller than the set track switching radius R, the result shows that the current specified path tracking task is completed, the navigation is stopped, or the track is switched to a next expected track, and otherwise, the second step is continuously carried out. The AUV three-dimension curve path tracking control method has the advantage that the AUV path tracking precision can be improved.