  In this paper, we analyze the light variation of KIC 8840638 using
high-precision time-series data from $Kepler$ mission. The analysis reveals
this target is a new Algol-type eclipsing binary system with a $\delta$ Scuti
component, not a pure single $\delta$ Scuti star previously known. The
frequency analysis of the short-cadence light curve reveals 95 significant
frequencies, most of which lie in a frequency range of 23$-$32 d$^{-1}$. Among
them, seven independent frequencies are detected in the typical frequency range
of $\delta$ Scuti stars and they are identified as pressure modes. Besides, the
orbital frequency $f_{orb}$ (=0.320008 d$^{-1}$) and its harmonics are also
detected directly in the frequency spectrum. The binary modellings derived from
the Wilson-Devinney code indicate the binary parameters are not affected by the
pulsations, and the binary system is in semi-detached configure with a mass
ratio of $q$ = 0.454, an inclination angle of 58 degrees, and a temperature
difference of larger than 4000 K between the two components. The derived
parameters suggest the primary of this system is a main-sequence star with
spectral type about A7V, while the secondary seems to be the coolest companion
star among the known semi-detached Algol systems, implying it may have stepped
into a highly evolved stage.
