The S1 stream surface inverse method for a single-stage axial transonic comPressor was developed and studied under the guidance of the quasi-three-dimensional viscous design theory, based on computational fluid dynamics (CFD), in order to establish and solve governing equations. The re--adjusted load distribution of the S1 stream surface was imposed to obtain a special profile for the rotor, which is known as S-shaping. This changed the structure and weaken the strength of the shock due to the Pre-comPression effect. In order to match the inlet flow angle of the downstream stator, inverse modification for multiple S1 stream surfaces of the stator blade was conducted in the Present study at the same time. As it is known, the S-shaped profile is commonly applied to supersonic flows. Therefore, NASA stage 37 was selected as the design case to verify whether the Present inverse method is effective and reliable. Stage 37 was re-designed by stacking five S1 stream surfaces. The profiles of these surfaces were renewed through the inverse design. The results revealed that, compared to the prototype, the aerodynamic performance of the re-designed one was apparently promoted within the stable working range. The adiabatic efficiency at the design point increased by approximately 0. 4%, and the Pressure ratio improved by approximately 4. 5%. In addition, analysis result for the characteristic line revealed that the performance of the redesigned blades at off-design points significantly improved.