In previous sketch recognition systems, curve has been fitted by a bit heuristic method. In this paper, we solved the problem by finding the optimal parameter of quadratic Bezier curve and utilize the error minimization between an input curve and a fitting curve by using iterative error minimization. First, we interpolated the input curve to compute the distance because the input curve consists of a set of sparse points. Then, we define the objective function. To find the optimal parameter, we assume that the initial parameter is known. Then, we derive the gradient vector with respect to the current parameter, and the parameter is updated by the gradient vector. This two steps are repeated until the error is not reduced. From the experiment, the average approximation error of the proposed algorithm was 0.946433 about 1400 synthesized curves, and this result demonstrates that the given curve can be fitted very closely by using the proposed fitting algorithm.