  The $^{11}$C($\alpha$, p) reaction is an important $\alpha$-induced reaction
competing with $\beta$-limited hydrogen-burning processes in high-temperature
explosive stars. We directly measured its reaction cross sections both for the
ground-state transition ($\alpha$, $p_{0}$) and the excited-state transitions
($\alpha$, $p_{1}$) and ($\alpha$, $p_{2}$) at relevant stellar energies 1.3 -
4.5 MeV by an extended thick-target method featuring time of flight for the
first time. We revised the reaction rate by numerical integration including the
($\alpha$, $p_{1}$) and ($\alpha$, $p_{2}$) contributions and also low-lying
resonances of ($\alpha$, $p_{0}$) using both the present and the previous
experimental data which were totally neglected in the previous compilation
works. The present total reaction rate lies between the previous ($\alpha$,
$p_{0}$) rate and the total rate of the Hauser-Feshbach statistical model
calculation, which is consistent with the relevant explosive hydrogen-burning
scenarios such as the $\nu p$-process.
