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The four-color (B, V, Rc, Ic) light curves of V776 Cas are presented and analyzed using the Wilson–Devinney method. It is discovered that V776 Cas is an early F-type (F2V) overcontact binary with a very high contact degree (f = 64.6%) and an extremely low-mass ratio (q = 0.130), which indicate that it is at the final evolutionary stage of cool short-period binaries. The mass of the primary and secondary stars are calculated to be M1 = 1.55(±0.04) M⊙, M2 = 0.20(±0.01) M⊙. V776 Cas is supposed to be formed from an initially detached binary system via the loss of angular momentum due to the magnetic wind. The initial masses of the present primary and secondary components are calculated to be M1i = 0.86(±0.10) M⊙ and M2i = 2.13(±0.04) M⊙. The observed–calculated curve exhibits a cyclic period variation, which is due to the light-travel time effect caused by the presence of a third component with a period of 23.7 years. The mass of the third component is estimated to be M3 = 1.04(±0.03) M⊙ and the orbital inclination of the third component is calculated to be i′ = 33.°1. The distance of the binary system to the mass center of the triple system is calculated to be = 3.45 AU. The presence of the close-in tertiary component may play an important role in the formation and evolution of this binary system by drawing angular momentum from the central system. [ABSTRACT FROM AUTHOR]