A Z-cut $LiNbO_3$ Mach-Zehnder waveguide modulator for optical wavelength measurement is fabricated. The waveguide is made by the proton-exchange method and the electrodes with a symmetric structure are 17.5mm long. After light is coupled to the Mach-Zehnder modulator and a ramp electrical voltage is applied, the photodector signal is sampled and processed by using Fast Fourier Transform(FFT). The center frequency of signals processed by FFT for a monochromatic input light in 1500nm-1590nm is shifted by the sampling frequency for every wavelength increment of 15nm. When two monochromatic light inputs are launched into the waveguide, the measured maximum wavelength resolution is 33nm. For better resolution, the length of electrodes should be increased significantly.