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 metre 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 analysed 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-fitting model with the stellar mass of M = 1.70 +/- 0.05 M-circle dot, the metallicity abundance of Z = 0.020 +/- 0.001, the age of 1.33 +/- 0.01 billion years and the period change rate 1/P.dP/dt = 1.06 x 10(-9) yr(-1), locating the star at the evolutionary stage close to the terminal age main sequence. The O-C diagram provides the period change rate of (1/P)(dP/dt) = 4.5(8) x 10(-7) 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.