In this paper, we consider a fractional integro differential equation (FrIDE) with continuous kernel in the space [ ] [Lp X C 0 ,T ], T 1, p 1. The FrNIDE, after integrating and using the properties of fractional integral will be transformed to Volterra – Fredholm integral equation of the second find (V-FIE) with continuous kernel in position. The existence and uniqueness solution of the V-FIE will be considered, using Banach fixed point theorem. Then, using a numerical method we have system of Volterra integral equations (SVIEs). The existence and uniqueness solution of the SVIEs will be considered. Then, we use the Toeplitz matrix method (TMM), as the best numerical method for solving the singular integral equation, to obtain a linear algebraic system (LAS). These LAS can be solved numerically. Finally, some numerical results, using maple program, will be obtained and the error estimate, in each case, is computed. Key Words: Fractional Integro Differential Equation, Volterra-Fredholm Integral Equation, Discontinuous Kernel, Toeplitz Matrix Method.