As the radius of curvature of curved optical waveguide gets smaller, the loss increases at the junction of linear-curved waveguide by the cross sectional mode mismatch. The concept of lateral offset has been used widely to minimize it, and simple method of maximum matching has been efficient for most cases of silica waveguide with low optical confinement and large radius of curvature. Here, we analyzed that the propagation mode characteristics of the lateral offset and propagation mode characteristics of general case with effective index method and Airy function solution. As the normalized frequency varies, mode characteristics changes near the boundary of 1/V=0.7 and the simple matching of gaussian profile might give -35% of error at most. We proposed improved method with a new correction factor to improve the mode mismatch problem of conventional methods for general cases, and showed the convenience and feasibility of this method for the calculation of the lateral offset.