Given a topological dynamical system $(X, T)$, a Borel cover
$\mathcal{U}$ of $X$ and a sub-additive sequence $\mathcal{F}$ of
real-valued continuous functions on $X$, two notions of
measure-theoretical pressure $P_\mu^- (T, \mathcal{U}, \mathcal{F})$
and $P_\mu^+ (T, \mathcal{U}, \mathcal{F})$ for an invariant Borel
probability measure $\mu$ are introduced. When $\mathcal{U}$ is an
open cover, a local variational principle between topological and
measure-theoretical pressure is proved; it is also established the
upper semi-continuity of P•+$(T, \mathcal{U}, \mathcal{F})$
and P•+$(T, \mathcal{U}, \mathcal{F})$ on the space of all
invariant Borel probability measures. The notions of
measure-theoretical pressure $P_\mu^- (T, X, \mathcal{F})$ and
$P_\mu^+ (T, X, \mathcal{F})$ for an invariant Borel probability
measure $\mu$ are also introduced. A global variational principle
between topological and measure-theoretical pressure is also
obtained.