  We consider principal subspace W({\Lambda}) of integrable highest weight
module L({\Lambda}) for quantum affine algebra
$U_q(\hat{\mathfrak{sl}}_{n+1})$. We introduce quantum analogues of the
quasi-particles associated with the principal subspaces for
$\hat{\mathfrak{sl}}_{n+1}$ and discover certain relations among them. By using
these relations we find, for certain highest weight {\Lambda}, combinatorial
bases of principal subspace W({\Lambda}) in terms of monomials of quantum
quasi-particles.
