We present charge-coupled device (CCD) photometry, light curve and time-series analysis of the classical nova V2275 Cyg (N Cyg 2001 No. 2). The source was observed for 14 nights in total in 2002 and 2003 using an R filter with the 1.5-m Russian-Turkish joint telescope (RTT150) at the TUBITAK National Observatory in Antalya, Turkey, as part of a large programme on the CCD photometry of cataclysmic variables. We report the detection of two distinct periodicities in the light curve of the nova: (a) P-1 = 0.314 49( 15) d [7.6 h], and (b) P-2 = 0.017 079(17) d [24.6 min]. The first period is evident in both 2002 and 2003 whereas the second period is only detected in the 2003 data set. We interpret the first period as the orbital period of the system and attribute the orbital variations to aspect changes of the secondary irradiated by the hot white dwarf (WD). We suggest that the nova was a supersoft X-ray source in 2002 and, perhaps, in 2003. The second period could be a quasi-periodic oscillation originating from the oscillation of the ionization front (due to a hot WD) below the inner Lagrange point or a beat frequency in the system as a result of the magnetic nature of the WD if steady accretion has already been re-established.