  Consider a proper geodesic metric space $(X,d)$ equipped with a Borel measure
$\mu.$ We establish a family of uniform Poincar\'e inequalities on $(X,d,\mu)$
if it satisfies a local Poincar\'e inequality ($P_{loc}$) and a condition on
growth of volume. Consequently if $\mu$ is doubling and supports $(P_{loc})$
then it satisfies a $(\sigma,\beta,\sigma)$-Poincar\'e inequality. If
$(X,d,\mu)$ is a $\delta$-hyperbolic space then using the volume comparison
theorem in \cite{BCS} we obtain a uniform Poincar\'e inequality with
exponential growth of the Poincar\'e constant. If $X$ is the universal cover of
a compact $CD(K,\infty)$ space then it supports a uniform Poincar\'e inequality
and the Poincar\'e constant depends on the growth of the fundamental group.
