We propose a novel compensation method based on a dispersion relation equation for the constrained interpolation profile (CIP) method. In our method, two additional operations are performed after the CIP calculation. One is to calculate the numerical attenuation constant $\widetilde\alpha$ and the numerical phase constant $\widetilde\beta$ from the dispersion relation equation using Newton-Raphson method. The other is product and sum operations to compensate for amplitude and phase from the calculated $\widetilde\alpha$ and the $\widetilde\beta$. As described in this paper, both the amplitude and the phase error have been compensated using our method.