A tapered electro-optic polymer waveguide is proposed and designed for coupling light between single-mode optical fiber and polymer waveguide. The tapered waveguide performs mode transformation between optical fiber mode and polymer waveguide mode by using a refractive index taper and a width taper with wedge profile. Wedge width taper possess smaller loss and is easy to make. The refractive index taper can be fabricated by utilizing a gray-scale mask lithography to control the UV light reaching each portion of the taper. The transmission loss of the tapers that depend on taper length,waveguide width and height,material loss are analyzed. The optimization of the design is discussed. The total power,mode distribution and its transformation through the taper are presented. The transmission loss of the taper is less than 0.37 dB,which results in an 8.78 dB insertion loss improvement and a low fiber-to-fiber component loss of 1.62 dB. The mode transformation efficiency is 83.7%.