In this study, new 3-dimensional mixed lubrication algorithm is developed. For a converged solution of the mixed lubrication problem, the asperity contact pressure is calculated for the amount of asperity contact occurred due to insufficient lubricant pressure, then the procedure adding the asperity contact pressure to the hydrodynamic pressure is continually iterated until the further asperity contact amount does not occur. This algorithm has advantage that the pressure and the film shape can be calculated from Reynolds equation for all mixed lubrication region without any specific boundary condition for edge of asperity contact region. In order to investigate usefulness of this algorithm, we conducted the mixed lubrication analysis for the spherical contact with a single asperity and a rough surface and showed that the developed algorithm gives a stable convergent solution even in which severe contact takes place due to asperity height being considerably large.