We propose an accurate modeling of the wavelength conversion process by dynamic tuning of a dielectric cavity. Since the process involves the long-distance propagation of light, the finite-difference time-domain (FDTD) method is not suitable for modeling of the wavelength conversion process owing to the numerical dispersion error of the FDTD method. The proposed modeling is based on the constrained interpolation profile (CIP) method, which was developed in the field of computational fluid dynamics for the purpose of reducing considerably the numerical dispersion error, and is formulated for a one-dimensional problem using an interpolation function of a higher order than that used in the original CIP method. Numerical experiments reveal that the proposed method can achieve accurate prediction of the wavelength conversion process even with a coarse grid model and is superior to both the original CIP method and the FDTD method.