There are many problems that restrict the work of the Mach-Zehnder modulator (MZM), including the lack of using various windows of wavelengths, the large half-wave voltage, and the small optical confinement factor. In this paper, a mathematical model for MZM based on lithium niobate (LN) is designed to solve these problems. In this model, a wide window of optical wavelength from visible-to-infrared (632.8-to-1560 nm) was utilized. Moreover, it achieved a better modulation with lower attenuation and a lower dispersion by the window (1550-1560) nm. The other window of optical wavelength is about (632.8-to-634 nm), and (646-to-647 nm) which can be used for short-haul applications to reduce attenuation and dispersion. Furthermore, a small length of the arm, about 2-3 mm, was utilized to accomplish a large change of the refractive index and lower applied voltage of up to 250 V. The small operation half-wave voltage achieved about 1.2 V leading to better switching of the MZM. In addition, a large optical confinement factor of ≤1 unitless was obtained. Even better performance of MZM was attained by using a suitable length arm of MZM of about 2 mm, along with an electric field of about 175 V/mm and 233 V/mm using poling at 100 V.