Abstract: To study homological dimensions, the finiteness of the weak global dimension of algebras was investigated by the theory of recollements. Assume that (D(Mod B), D(Mod A), D(Mod C)) is a standard recollement of derived categories. Results show that if the standard recollements satisfy some conditions, then the weak global dimension of the algebra A is finite if and only if so are the algebras B and C. As an application, results show that the finiteness of the weak global dimension of an algebra is invariant under derived equivalent.