  In this paper, let $(\mathcal{A},\mathcal{B},\mathcal{C})$ be a recollement
of extriangulated categories. We introduce the global dimension and extension
dimension of extriangulated categories, and give some upper bounds of global
dimensions (resp. extension dimensions) of the categories involved in
$(\mathcal{A},\mathcal{B},\mathcal{C})$, which give a simultaneous
generalization of some results in the recollement of abelian categories and
triangulated categories.
