An \({\varvec{hp}}\) -version fractional spectral collocation method is implemented to weakly singular Volterra integro-differential equations with vanishing delay. The main idea is to seek an approximate solution in a fractional polynomial space on each subinterval. For a class of constrained meshes depending on the delay function, an \({\varvec{hp}}\) -version error estimate in a weighted \({\varvec{H}}^1\) norm is obtained, which shows that even if the exact solution has weak singularity, the error can decay exponentially in certain cases. Numerical examples are conducted to verify the theoretical results.
