Based on an improvement of the Karman-Pohlhausen's method, using nonlinear polynomial fitting and numerical integral, the axial distributions of pressure and its gradient in an axisymmetric rigid vessel with stenosis were obtained, and the distributions related to Reynolds number and the geometry of stenotic vessel were discussed. It shows that with the increasing of stenotic degree or Reynolds number, the fluctuation of pressure and its gradient in stenotic area is intense rapidly, and negative pressure occurs subsequently in the diverging part of stenotic area. Especially when the axial range of stenosis extends, the flow of blood in the diverging part will be more obviously changed. In higher Reynolds number or heavy stenosis, theoretical calculation is mainly in accordance with past experiments.