  Observations for the $\delta$ Scuti star AN Lyn have been made between 2008
and 2016 with the 85-cm telescope at Xinglong station of National Astronomical
Observatories of China, the 84-cm telescope at SPM Observatory of Mexico and
the Nanshan One meter Wide field Telescope of Xinjiang Observatory of China.
Data in $V$ in 50 nights and in $R$ in 34 nights are obtained in total. The
bi-site observations from both Xinglong Station and SPM Observatory in 2014 are
analyzed with Fourier Decomposition to detect pulsation frequencies. Two
independent frequencies are resolved, including one non-radial mode. A number
of stellar model tracks are constructed with the MESA code and the fit of
frequencies leads to the best-fit model with the stellar mass of $M = 1.70 \pm
0.05~\mathrm{M_{\odot}}$ , the metallicity abundance of $Z = 0.020 \pm 0.001$,
the age of $1.33 \pm 0.01$ billion years and the period change rate $1/P\cdot
\mathrm{d}P/\mathrm{d}t =1.06 \times 10^{-9} ~\mathrm{yr^{-1}} $, locating the
star at the evolutionary stage close to the terminal age main sequence (TAMS).
The O-C diagram provides the period change rate of $1/P \cdot \mathrm{d}P
/\mathrm{d}t =4.5(8)\times10^{-7}~\mathrm{yr^{-1}}$. However, the period change
rate calculated from the models is smaller in two orders than the one derived
from the O-C diagram. Together with the sinusoidal function signature, the
period variations are regarded to be dominated by the light-travel time effect
of the orbital motion of a three-body system with two low-luminosity
components, rather than the stellar evolutionary effect.
