The paper is devoted to the study of Hyers, Ulam and Rassias types of stability for a class of nonlinear Volterra integral equations. Both Hyers-Ulam-Rassias stability and Hyers-Ulam stability are obtained for such a class of Volterra integral equations when considered on a finite interval. In addition, for corresponding Volterra integral equations on infinite intervals the Hyers-Ulam-Rassias stability is also obtained.