  In this article we propose a scheme for solving the coupled time-fractional
nonlocal diffusion problem. The scheme consist of fractional Crank-Nicolson
method with Galerkin finite element method (FEM) and Newton's method. We derive
\emph{a priori} error estimates for fully-discrete solutions in $L^2$ and
$H^1_0$ norms. Results based on the usual finite element method are provided to
confirm the theoretical estimates.
