The current-potential relation for a catalytic electrode reaction at a hemispherical ultramicroelectrode has been deduced. According to the peak current or the limiting diffusion current, a method for measuring the catalytic rate constant has been proposed. As an application, the sixth electrochemical reduction of fullerene, C-60, has been investigated. The experimental results show that the sixth reduction of C-60 is a catalytic process. The catalytic rate constant was determined by the method described in this paper.