Orbital-Period Variations and Photometric Analysis for the Neglected Contact Binary EH Cancri

New CCD photometry for the eclipsing binary EH Cnc was made from 2009 to 2011, and five new eclipsing times are presented. Through using the updated Wilson-Devinney code, we first deduced the photometric solution at chi(2) = 0.9906. The results show that EH Cnc is a W-type contact binary, whose mass ratio and overcontact degree are q = 2.51 (+/- 0.02) and f = 27.7% (+/- 3.4%), respectively. By analyzing the O - C curve of EH Cnc, it is found that there exists a secular-period decrease with a cyclic variation. The period and semiamplitude are P-3 = 16.6 (+/- 0.4) yr and A = 0.0032 days (+/- 0.0003 days), respectively. This kind of cyclic variation may probably be attributed to the light-time effect via the presence of an unseen third body, because the values of Delta Q(1,2) are much smaller than the typical one for close binaries. The orbital period of EH Cnc continuously decreases at a rate of dP/dt = -1.01 (+/- 0.05) x 10(-7) days yr(-1). This kind of secular period decrease may result from mass transfer from the primary to the secondary, accompanied by mass and angular momentum loss from the system. With the orbital period decreasing, the inner and outer Roche lobes will shrink, causing the contact degree to increase. Finally, binaries with decreasing periods, such as EH Cnc, will evolve into deep-contact configurations.