Ultra-short pulse (picosecond) anti-Stokes laser can be obtained by using Raman frequency converter in a crystal medium by the coherent anti-Stokes Raman scattering effect. The crystalline Raman frequency converter based on the pump-probe method can realize the collinear interaction of coherent anti-Stokes Raman scattering, thus effectively improving the conversion efficiency of the anti-Stokes light. Theoretical simulation is an important means to study laser operation. Coupled wave equation is widely used to study the characteristics of Raman laser and anti-Stokes laser. Although the coupling wave theory of anti-Stokes Raman frequency shifter reported previously can reflect the operation law of the frequency shifter, the optimization of the frequency shifter and the influence of the frequency shifter parameters on the output characteristics of anti-Stokes laser have not been reported so far. In this paper, the picosecond anti-Stokes Raman frequency converter based on the pump-probe method is studied theoretically. Considering the generation of the first Stokes light in the probe channel and the second Stokes light in the pump channel, the coupled wave equation of the collinear picosecond anti-Stokes Raman frequency converter is established under the plane wave approximation. Without loss of generality, four dimensionless comprehensive parameters are introduced to normalize the equations. A set of universal theoretical curves describing the operation of the Raman frequency converter is obtained. The numerical solutions of the equations show that the performance of the Raman frequency converter mainly depends on three parameters: the normalized phase mismatch parameter ΔK, the normalized Raman gain coefficient G, and the energy ratio of the probe light to the fundamental light r_probe. The reasonable values of normalized variables are determined when the high efficiency anti-Stokes conversion is realized. Experimental data are used to verify the correctness of the theoretical model. The theoretical value of the anti-Stokes conversion efficiency is basically consistent with the literature data. The normalized coupled wave theory proposed in this paper is helpful in understanding the operation law of the picosecond anti-Stokes Raman frequency shifter, and has guiding significance for the design of the frequency converter.