In this paper, we prove the existance of subspace-diskcyclic C0-semigroups on any infinite-dimensional separable Banach space. We state that diskcyclic C0-semigroups are subspace-diskcyclic. Also, we establish some criteria for subspace-diskcyclic C0-semigroups. Most of these criteria are based on non-empty relatively open sets and some of them are based on dense sets.