In this manuscripts, we consider the coupled differential-integral equations including the variable-order Caputo fractional operator. To solve numerically these type of equations, we apply the shifted Jacobi-Gauss collocation scheme. Using this numerical method a system of algebraic equations is constructed. We solve this system with a recursive method in the nonlinear case and we solve it in linear case with algebraic formulas. Finally, for the high performance of the suggested method three Examples are illustrated.