OGLE-LMC-DPV-065 is an interacting binary whose double-hump long photometric cycle remains hitherto unexplained. We analyze photometric time series available in archive datasets spanning 124 years and present the analysis of new high-resolution spectra. A refined orbital period is found of 10fd0316267 $pm$ 0fd0000056 without any evidence of variability. In spite of this constancy, small but significant changes in timings of the secondary eclipse are detected. We show that the long period continuously decreases from 350 to 218 days during 13 years, then remains almost constant for about 10 years. Our study of radial velocities indicates a circular orbit for the binary and yields a mass ratio of 0.203 $pm$ 0.001. From the analysis of the orbital light curve we find that the system contains 13.8 and 2.81 msun stars of radii 8.8 and 12.6 rsun and absolute bolometric magnitudes -6.4 and -3.0, respectively. The orbit semi-major axis is 49.9 rsun and the stellar temperatures are 25460 K and 9825 K. We find evidence for an optically and geometrically thick disk around the hotter star. According to our model, the disk has a radius of 25 rsun, central and outer vertical thickness of 1.6 rsun and 3.5 rsun, and temperature of 9380 K at its outer edge. Two shock regions located at roughly opposite parts of the outer disk rim can explain the light curves asymmetries. The system is a member of the double periodic variables and its relatively high-mass and long photometric cycle make it similar in some aspects to $beta$ Lyrae.
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