This work is concerned with a class of Volterra functional integro-differential equations. Based on the \(\theta\) -invariant mesh, the multistep collocation schemes are constructed. Then the optimal global and local superconvergence orders of the proposed method are detailedly analyzed. It turns out that for a set of suitable chosen collocation parameters, the convergence orders of d-step and n-point collocation method may reach \(n+d\) in global and \(2n+d-1\) at the mesh points, which are much higher than the classical one-step collocation method. Additionally, compared with existing works, no extra starting procedure is needed for the proposed multistep collocation method. Several illustrative numerical tests are provided to support the theoretical results in the final section.
