DI Hya is a short-period eclipsing binary and its classification has been discussed by several authors. New four-color light curves were obtained and have been analyzed together with the data from Manimanis & Niarchos simultaneously using the W-D method. The binary turns out to be a near-contact system where both components are filling or nearly filling their critical Roche lobes. The secondary has a temperature difference of Delta T similar or equal to-2800 K. The orbital period investigation has been ignored so far. All charge-coupled devices (CCD)and pe times of light minima are used for period analysis, showing that a cyclic variation with a short period of 1.46 years and a small semi-amplitude of 0.0034 days and a downward parabolic variation with a rate of P = -2.98(+/- 0.32)x 10(-7)days yr(-1). The short period and small semi-amplitude cyclic variations were analyzed for the light-travel time effect via the presence of a close-in tertiary binary with an orbital separation shorter than 1.57(+/- 0.31) au. Orbital properties of this close-in companion should provide valuable information on the formation of this short-period binary and stellar dynamical interaction. The downward parabolic change may be caused by angular momentum loss via an enhanced stellar wind of the more evolved secondary star.