A new approach for parabolic curve detection is presented based on Hough transforms. This approach uses the vertices of the curve as the detecting parameters which also indicate the position of the maximum curvature. Evidence for the transformation is gathered from the edge gradient obtained from an edge enhancement operator. The Sobel operator is used for edge enhancement. For the detection of parabolic curves in any orientation, a coordinate transformation matrix is used to derive a new parabolic equation which involves the edge gradient information. In the proposed algorithm, parabolic curves in any orientation are detected by using a 3D accumulator array. The new algorithm, therefore reduces the accumulator size from 4D accumulator array if an ordinary Hough transform for parabola detection is used. The reduced parameter space of the proposed algorithm improves the processing time and decreases storage requirement for the detection of parabolic curves. The paper reports on the accuracy obtained when this approach is used on natural and synthetic images containing parabolic and other curves.