New CCD photometry is presented for the hot overcontact binary DK Cyg together with reasonable explanations for the light and period variations. Historical light and velocity curves from 1962 to 2012 were simultaneously analyzed with the Wilson-Devinney (W-D) synthesis code. The brightness disturbances were satisfactorily modeled by applying a magnetic cool spot on the primary star. Based on 261 times of minimum light that include 116 new timings and span more than 87 years, a period study reveals that the orbital period has varied due to a periodic oscillation superimposed on an upward parabola. The period and semi-amplitude of the modulation are about 78.1years and 0.0037days, respectively. This detail is interpreted as a light-travel-time effect due to a circumbinary companion with a minimum mass of M_3_=0.065M_{sun}, within the theoretical limit of ~0.07M{sun}_ for a brown dwarf star. The observed period increase at a fractional rate of +2.74x10^-10^ is in excellent agreement with that calculated from our W-D synthesis. Mass transfer from the secondary to the primary component is mainly responsible for the secular period change. We examined the evolutionary status of the DK Cyg system from the absolute dimensions.