  Multi-color light curves and radial velocities for TYC\,1031\,1262\,1 have
been obtained and analyzed. TYC\,1031\,1262\,1 includes a Cepheid with a period
of 4.15270$\pm$0.00061 days. The orbital period of the system is about
51.2857$\pm$0.0174 days. The pulsation period indicates a secular period
increase with an amount of 2.46$\pm$0.54 min/yr. The observed B, V, and R
magnitudes were cleaned for the intrinsic variations of the primary star. The
remaining light curves, consisting of eclipses and proximity effects, are
obtained and analyzed for orbital parameters. The system consists of two
evolved stars, F8II+G6II, with masses of M$_1$=1.640$\pm$0.151 {\Msun} and
M$_2$=0.934$\pm$0.109 {\Msun} and radii of R$_1$=26.9$\pm$0.9 {\Rsun} and
R$_2$=15.0$\pm$0.7 {\Rsun}. The pulsating star is almost filling its
corresponding Roche lobe which indicates the possibility of mass loss or
transfer having taken place. We find an average distance of d=5070$\pm$250\,pc
using the BVR and JHK magnitudes and also the V-band extinction. Kinematic
properties and the distance to the galactic plane with an amount of 970 pc
indicate that it belongs to the thick-disk population. Most of the observed and
calculated parameters of the TYC\,1031\,1262\,1 lead to a classification of an
Anomalous Cepheid.
