  The {\it Kepler} light curve of KIC 4739791 exhibits partial eclipses,
inverse O'Connell effect, and multiperiodic pulsations. Including a starspot on
either of the binary components, the light-curve synthesis indicates that KIC
4739791 is in detached or semi-detached configurations with both a short
orbital period and a low mass ratio. Multiple frequency analyses were performed
in the light residuals after subtracting the binarity effects from the original
{\it Kepler} data. We detected 14 frequencies: six in the low-frequency region
(0.1$-$2.3 d$^{-1}$) and eight in the high-frequency region (18.2$-$22.0
d$^{-1}$). Among these, six high frequencies with amplitudes of 0.62$-$1.97
mmag were almost constant over time for 200 d. Their pulsation periods and
pulsation constants are in the ranges of 0.048$-$0.054 d and 0.025$-$0.031 d,
respectively. In contrast, the other frequencies may arise from the alias
effects caused by the orbital frequency or combination frequencies. We propose
that KIC 4739791 is a short-period R CMa binary with the lowest mass ratio in
the known classical Algols and that its primary component is a $\delta$ Sct
pulsating star. Only four R CMa stars have been identified, three of which
exhibit $\delta$ Sct-type oscillations. These findings make KIC 4739791 an
attractive target for studies of stellar interior structure and evolution.
