  Given a bounded domain $\Omega \subset {\mathbb R}^{n}$ with $n\ge2$, let
$\phi $ is a Young function satisfying the doubling condition with the constant
$K_\phi<2^{n}$.
  If $\Omega$ is a John domain, we show that $\Omega $ supports a $(\phi_{n},
\phi)$-Poincar\'e inequality.
  Conversely, assume additionally that $\Omega$ is simply connected domain when
$n=2$ or a bounded domain which is quasiconformally equivalent to some uniform
domain when $n\ge3$. If $\Omega$ supports a $(\phi_n, \phi)$-Poincar\'e
inequality, we show that it is a John domain.
