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V1082 Sgr is a cataclysmic variable with accretion luminosity above$10^{34}$erg s$^{-1}$, indicating a mass transfer rate above$10^{-9}M_{\odot}$yr$^{-1}$. However, its K type companion was suggested to beunder-filling its Roche lobe (RL), making the high mass transfer rate amystery. In this work we propose a possible model to explain this discrepancy.The system is proposed to be an intermediate polar, with its K type companionfilling its RL. The mass of the white dwarf star is evaluated to be$0.77\pm0.11M_{\odot}$ from both X-ray continuum fitting and Fe line flux ratiomeasurements. We make numerical simulations to search for the possibleprogenitors of the system. The results show that a binary with an initial1.5--2.5$M_{\odot}$ companion in a 1--2 day orbit (or an initial1.0--1.4$M_{\odot}$ companion in a 3.2--4.1 day orbit) may naturally evolve toa cataclysmic variable with a $\sim 0.55 \pm 0.11M_{\odot}$, Roche-lobe fillingcompanion in a 0.86 day orbit. The effective temperature of the donor star, themass transfer rate, and the derived V band magnitude are all consistent withprevious observations.

V1082-Sgr: A magnetic cataclysmic variable with a lobe-filling companion star