A traveling-wave CPW(coplanar waveguide) electrode with abruptly broken input/output-taper for LiNbO$_3$optical modulator was designed and fabricated. The electrical characteristics of traveling-wave electrode on z-cut LiNbO$_3$crystal with SiO$_2$buffer layers were measured by network analyzer. To confirm the possibility of the electro-optic modulator electrode, detailed calculations of the impedance, microwave effective index and attenuation constants are presented as a function of the microwave electrode thickness, but the buffer layer thickness is fixed as 1${mu}{ extrm}{m}$. These characteristics are discussed from the viewpoint of the device optimization and are expected to be design guides for the LiNbO$_3$modulator’s electrodes.