New photometric data of EQ?Tau observed in 2010 and 2013 are presented. Light curves obtained in 2000 and 2004 by Yuan & Qian and 2001 by Yang & Liu, together with our two newly determined sets of light curves, were analyzed using the Wilson-Devinney code. The five sets of light curves exhibit very obvious variations, implying that the light curves of EQ?Tau show a strong O'Connell effect. We found that EQ?Tau is an A-type shallow contact binary with a contact degree of f = 11.8%; variable dark spots on the primary component of EQ?Tau were also observed. Using 10 new times of minimum light, together with those collected from the literature, the orbital period change of EQ?Tau was analyzed. We found that its orbital period includes a secular decrease (dP/dt = –3.63 × 10–8?days?yr–1) and a cyclic oscillation (A 3 = 0.0058?days and P 3 = 22.7?yr). The secular increase of the period can be explained by mass transfer from the more massive component to the less massive one or/and angular momentum loss due to a magnetic stellar wind. The Applegate mechanism cannot explain the cyclic orbital period change. A probable transit-like event was observed in 2010. Therefore, the cyclic orbital period change of EQ?Tau may be due to the light time effect of a third body.
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