In this paper a high order finite difference method is constructed to solve the elastohydrodynamic lubrication line contact problems, whose cavitation condition is handled by the penalty method. The highly nonlinear equations from the discretization of the high order finite difference method are solved by the trust-region dogleg algorithm. In order to reduce the numerical dissipation and dispersion brought by the high order upwind finite difference scheme, a high order biased upwind finite difference scheme is also presented. Our method is found to achieve more accurate solutions using just a small number of nodes compared to the multilevel methods combined with the lower order finite difference method.