In this paper, we introduce a new class $\sum ^{*}_{p} (A,B,k)_{a,c}$ for $-1\leqslant B<A \leqslant1$ which consists of hypergeometric meromorphic functions of the form $L^{*}_{p}(a,c)f(z)= \frac{1}{z^{p}}+ \sum_{n=0}^{\infty}\frac{(a)_{n+2}}{(c)_{n+2}} a_{n+p}z^{n+p}$ in $U^{*} = \{z : 0 < \left|z\right| < 1\}$. We determine sufficient conditions, distortion properties, radii of starlikeness and convexity and inclusion properties for the class $L^{*}_{p}(a,c)f(z)$.