The Non-periodic Optical Superlattice (NOS) structure was designed by using the the Nonlinear Conjugate-Gradient(NCG) algorithm, and the applicability in the NOS structure of the relative tolerance function mentioned in Ref.[12] was studied. The results show that, this relative tolerance function can apply to the NOS structure well, and the NOS structure is more general to compare with the Aperiodic Optical Super-lattice(AOS) which is used in Ref. [12]. When u′2(xn) and n keep a good linear relationship, the relative tolerance function curve calculated in the NOS structure is nearly coincident with that mentioned in Ref.[12], which shows that a Quasi-Phase-Matching(QPM) is well satisfied in the NOS structure. The applicability in the NOS structure of the relative tolerance function which is under the case of phase mismatching was also furtherly investigated by introducing the random error in the sample. The results show that, the relative tolerance function curve calculated in the NOS structure is not coincident with the standard curve under the case of phase mismatching, and as the mismatching degree increases, the relative tolerance function curves exhibit a larger deviation from the standard one. The applicable scope of Un-depleted Pump Approximation (UPA) can be approximately calculated by using the relative tolerance function when this deviation is not large.