The first ground-based BVR photometric observations of the recently discovered eclipsing binary V744 Cas are presented. From these measurements, timings for two primary and one secondary minima have been calculated. The light curves of the system were analyzed by using the Wilson-Devinney program. The analysis shows that the system is detached with two similar components of spectral type A2V, and the orbit is eccentric (e = 0.0662 +/- 0.0005). The longitude of the periastron (w) was found significantly different for two different light curves (ours and that of Hipparcos), which is strongly suggestive of an apsidal motion with a period of about 425 +/- 68 yr. This makes V744 Cas an important candidate for studies of apsidal motions. The first estimate of the absolute dimensions place the system close to the terminal age of the main sequence (TAMS) in the HR diagram. The distance from the spectroscopic parallax (d = 740 +/- 10 pc) was found to be slightly larger than the Hipparcos distance of d = 610 +/- 400 pc. (c) 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.