n this work, we present a new boundary conditions for fractional cubic spline (FCS) model for solving fractional Volterra-integral equations. We reduced the problem to a set of a linear systems by using fractional continuity conditions. Convergence analysis proved to solve fractional Volterra-integral equations by obtained linear systems, to determine fractional spline derivatives, we applied the Caputo fractional derivative. The process is detailed and computed with three computational examples, and the results show that it is both effective and simple to use. Moreover, the results are compared with the methods in [1 ], [ 2 ] and [4].