The structure of Ti:LiNbO$_3$optical waveguide with a mode size far different from that of single mode optical fiber has been optimized by tapering the waveguide ends. This work was focused on determining the optimized sets of parameters for the fabrication of low-loss Ti indiffused optical waveguides in LiNbO$_3$. Numerical and analytical modeling were applied to simulate the guiding quality and to determine the mode sizes. Based on these modeling results, new waveguide structures with tapered ends have been defined, fabricated and characterized in the respect of the coupling of fiber to Ti-indiffused LiNbO$_3$waveguide.