A fractal model of normal contact stiffness of orthotropic joint with lubrication medium is proposed. The model adopts the Hertz contact theory with elliptic correction factor， and based on the mean Reynolds equation with lateral leakage of the lubrication medium. Then， deducing the analytical relationship between the solid contact stiffness and the fluid stiffness. By means of analyzing the influence of different factors on the normal contact stiffness of joint， it is found that when the dimensionless real contact area between solids is less than 0.05， the normal contact stiffness of joint is mainly affected by fluid stiffness. With the occurrence of lateral leakage of lubrication medium， real contact area between solids is gradually large， and the influence of solid contact stiffness on the normal contact stiffness of the joint becomes more and more significant. Giving different normal preload and comparing the first three orders of natural frequencies obtained from experiments and finite element analysis， the maximum relative error between frequencies is 4.11%， which proves that the model proposed in this paper can predict the contact performance of joint more accurately