In this paper, we introduce and investigate three interesting subclass $\sum^*_\vartheta(\lambda,\alpha)$, $\sum^B_\vartheta(\beta,\alpha)$ and $\tilde\sum^*_\vartheta(\alpha,\beta)$ of meromorphic and bi-univalent functions on $\Delta=\{z\in\Bbb C:|z|>1\}$, obtain their coefficient estimates. The results presented in this paper generalize the recent work of several earlier authors.