  We consider principal subspaces $W_{L(k\Lambda_0)}$ and $W_{N(k\Lambda_0)}$
of standard module $L(k\Lambda_0)$ and generalized Verma module $N(k\Lambda_0)$
at level $k\geq 1$ for affine Lie algebra of type $B_2^{(1)}$. By using the
theory of vertex operator algebras, we find combinatorial bases of principal
ubspaces in terms of quasi-particles. From quasi-particle bases, we obtain
character formulas for $W_{L(k\Lambda_0)}$ and $W_{N(k\Lambda_0)}$.
