A new method of analyzing three waves interaction in nonlinear periodically poled crystals(PP-crystals)on the theorem of quasi-phase-matching,called the vector superposing method is presented. By using of the characteristic curve of interactive electric field,this method can clearly illustrate the principle of the electric field changing in the second harmonic generation process inside the nonlinear PP-crystals. The method can not only describe the physics phenomenon clearly but also get concise results. These results are similar with former Fourier's transform and can be used to research the influence of various errors for the efficiency of SHG in ferroelectric domain-inverted gratings .The method also establishes the theoretical foundation for realizing the new method of QPM.