  We investigated thermoelectric power $S(T)$ of MgB$_{2-x}$Be$_{x}$ ($x=0$,
0.2, 0.3, 0.4, and 0.6). $S(T)$ decreases systematically with $x$, suggesting
that the hole density increases. Our band calculation shows that the increase
occurs in the $\sigma $-band. With the hole-doping, $T_{c}$ decreases.
Implication of this phenomenon is discussed within the BCS framework. While the
Mott formula explains only the linear part of $S(T)$ at low temperature,
incorporation of electron-phonon interaction enables us to explain $S(T)$ over
wide temperature range including the anomalous behavior at high temperature.
