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 $ u p$-process.
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