Extracting axis of 3D blood vessel images is very important and useful to quantify blood vessel in medical diagnosis. According to blood vessel features, we constructed the energy constraint equation of blood vessel. The initial skeleton curve of blood vessel images obtained by thinning algorithm dynastically converges to the position of the axis under energy constraint equation and along gradient direction of the distance field of blood vessel images. When the equation energy reaches a minimum value, the initial skeleton curve also fixes in the axis position at this time. Experimental results show that the position of the blood vessels axis extracted by this method is accurate, and the axis preserves topology and connectivity.