We study the $Q$-Kostka polynomials $L_{λμ}(t)$ by the vertex operator realization of the $Q$-Hall-Littlewood functions $G_λ(x;t)$ and derive new formulae for $L_{λμ}(t)$. In particular, we have established stability property for the Q-Kostka polynomials. We also introduce spin Green polynomials $Y^λ_μ(t)$ as both an analogue of the Green polynomials and deformation of the spin irreducible characters of $\mathfrak S_n$. Iterative formulas of the spin Green polynomials are given and some favorable properties parallel to the Green polynomials are obtained. Tables of $Y^λ_μ(t)$ are included for $n\leq7.$