In this work, the photometric data from the American Association of Variable Star Observers are collected and analyzed on the SX Phoenicis star DY Pegasi (DY Peg). From the frequency analysis, we get three independent frequencies: $f_0 = 13.71249 rm{c days^{-1}}$, $f_1 = 17.7000 rm{c days^{-1}}$, and $f_2 =18.138 rm{c days^{-1}}$, in which $f_0$ and $f_1$ are the radial fundamental and first overtone mode, respectively, while $f_2$ is detected for the first time and should belong to a nonradial mode. The $O-C$ diagram of the times of maximum light shows that DY Peg has a period change rate $(1/P_0)(mathrm{d} P_0/mathrm{d} t) = -(5.87 pm 0.03) times 10^{-8} mathrm{yr^{-1}}$ for its fundamental pulsation mode, and should belong to a binary system that has an orbital period $P_{mathrm{orb}} = 15425.0 pm 205.7 mathrm{days}$. Based on the spectroscopic information, single star evolutionary models are constructed to fit the observed frequencies. However, some important parameters of the fitted models are not consistent with that from observations. Combing with the information from observation and theoretical calculation, we conclude that DY Peg should be an SX Phoenicis star in a binary system and accreting mass from a dust disk, which was the residue of its evolved companion (most probably a hot white dwarf at the present stage) produced in the asymptotic giant branch phase. Further observations are needed to confirm this inference, and it might be potentially a universal formation mechanism and evolutionary history for SX Phoenicis stars.
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