The purpose of this paper is to present the following linear generalization of Gronwall's inequality: Let the function x be continuous and non-negative on the interval [0,T]. If \[ x(t)\leq \Phi (t)+M\int^{t}_{0}\int^{t_ m}_{0}...\int^{t_ 1}_{0}[x(s)/(t_ 1-s)^{\alpha}]ds dt_ 1...dt_ m,\quad t\in [0,T], \] where \(\alpha 0\) is constant, and \(\Phi\) (t) is a non-negative, non-decreasing continuous function in t, \(t\in [0,T]\), then \[ x(t)\leq \Phi (t)E_{1-(\alpha -m)}(M\Gamma (1-\alpha)t^{1- (\alpha -m)}),\quad t\in [0,T], \] where \(E_{1-\beta}(z)\) is the Mittag-Leffler function defined by \[ E_{1- \beta}(z)=\sum^{\infty}_{n=0}z^ n/\Gamma (n(1-\beta)+1). \] The authors also obtain a discrete form of Gronwall's inequality. At the end of the paper, there is presented an application to the integro- differential equation \(y'(t)=F(t,y(t),\psi (t)),\quad t\in [0,T],\quad y(0)\quad given,\) where \[ \psi (t)=\int^{t}_{0}[k(t,s,y(s))/(t- s)^{\alpha}]ds,\quad 0<\alpha <1, \] and F, k are sufficiently smooth to guarantee the existence of a unique solution y which has a bounded second derivative.