  In this paper, we construct the Virasoro type additional symmetries of a kind
of constrained multi-component KP hierarchy and give the Virasoro flow equation
on eigenfunctions and adjoint eigenfunctions. It can also be seen that the
algebraic structure of the Virasoro symmetry is kept after discretization from
the constrained multi-component KP hierarchy to the discrete constrained
multi-component KP hierarchy.
