  We reported a cyclic variation of $O-C$ diagram with a semi-amplitude of
0.0033 days and a period of 1.05 years for the pulsating eclipsing binary HZ
Dra. The cyclic variation can be explained by the light travel-time effect via
the presence of a close-in third body orbiting around HZ Dra in an elliptical
orbit with a maximum semi-major axis of 0.92 au. Based on the W-D code, the
contribution of the third light to the total system is determined to be 29
$\%$, which is in agreement with the estimated value. Our light curve modelling
indicates an evolving hot and cool spot on the surface of the primary and
secondary components, respectively. Their positions are roughly symmetrical to
the inner Lagrangian point L1, which could be used to explain the variation in
the O$^{'}$Connell effect. Our frequency analysis detects 1 radial p-mode, 7
non-radial p-modes and 1 non-radial g-mode. In addition, a total of 6
multiplets are identified, spaced by the orbital frequency, which can be
explained as a tidally split mode caused by the equilibrium tides of the close
binary system with a circular orbit. These pulsating features suggest that the
primary of HZ Dra is a $\delta$ Scuti star, pulsating in both p- and g-mode and
influenced by tidal forces.
