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/Pcdot 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.
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