The hydrostatic journal bearing’s recess pressure is to be determined using a novel approach. This method treats the circumferential bearing lands on both sides of recesses as infinitely long bearings, and the axial bearing lands on both sides of recesses as infinitely short bearings. The Newton–Cotes integral formula is used to solve the definite integration. By this simplification, a new analytical expression of recess pressure considering the hydrodynamic effect on bearing land is obtained. The recess pressure versus eccentricity, supply oil pressure, recess wrap angle, and attitude angle solved by the new method is compared with that calculated by the finite difference method and Liang’s method from two kinds of four-recess hydrostatic journal bearing compensated by capillary restrictor. The results indicate that the new process has high accuracy and its precision is not almost affected by the parameters change. Moreover, the new method has low time consumption.