We propose a new method for error-bounded B-spline curve approximation based on dominant point selection. The method first selects from the given points initial dominant points that govern the overall shape of the point set. It then computes a knot vector using the dominant points and performs B-spline curve fitting to all the given points. If the fitted B-spline curve cannot approximate the points within a specified tolerance, the method selects more points as dominant points and repeats the curve fitting process. The knots are determined in each iterative process by averaging the parameters of the dominant points. The shape index of a point set is introduced to facilitate the dominant point selection during the iterative curve fitting process. Compared with conventional methods presented for B-spline curve approximation, the proposed method requires much less control points to approximate the given point set with the desired shape fidelity.