A fast yet accurate method for analyzing a wire antenna of arbitrary shape is developed. In addition to the straight line in a wire grid model, a new canonical element, namely, an arc of constant radius of curvature is introduced. For a curvilinear antenna, combination of bent and unbent lines could substantially reduce the fitting error. A technique is devised that solves the vector wave equation on the surface of an arced segment as simple as if it were a straight one. As each segment is relatively long in the enhanced mode, symmetry of the impedance matrix can be fully utilized to speed up the computation. The scheme is used to study some typical curvilinear antennas and excellent results are observed.