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Context. To add to the growing collection of well-studied double periodic variables (DPVs) we have carried out the first spectroscopic and photometric analysis of the eclipsing binary DQ Velorum to obtain its main physical stellar and orbital parameters. Aims. Combining spectroscopic and photometric observations that cover several orbital cycles allows us to estimate the stellar properties of the binary components and the orbital parameters. We also searched for circumstellar material around the more massive star. Methods. We separated DQ Velorum composite spectra and measured radial velocities with an iterative method for double spectroscopic binaries. We obtained the radial velocity curves and calculated the spectroscopic mass ratio. We compared our single-lined spectra with a grid of synthetic spectra and estimated the temperature of the stars. We modeled the V-band light curve with a fitting method based on the simplex algorithm, which includes an accretion disc. To constrain the main stellar parameters we fixed the mass ratio and donor temperature to the values obtained by our spectroscopic analysis. Results. We obtain a spectroscopic mass ratio q = 0.31 ± 0.03 together with donor and gainer masses Md = 2.2 ± 0.2 M☉, Mg = 7.3 ± 0.3 M☉, the radii Rd = 8.4 ± 0.2 R☉, Rg = 3.6 ± 0.2 R☉ and temperatures Td = 9400 ± 100 K, Tg = 18 500 ± 500 K for the stellar components. We find that DQ Vel is a semi-detached system consisting of a B3V gainer and an A1III donor star plus an extended accretion disc around the gainer. The disc is filling 89% of the gainer Roche lobe with a temperature of 6580 ± 300 K at the outer radius. It has a concave shape that is thicker at its edge (de = 0.6 ± 0.1 R☉) than at its centre (dc = 0.3 ± 0.1 R☉). We find a significant sub-orbital frequency of 0.19 d-1 in the residuals of the V-band light curve, which we interpret as a pulsation of an slowly pulsating B-type (SPB) of a gainer star. We also estimate the distance to the binary (d ~ 3.1 kpc) using the absolute radii, apparent magnitudes, and effective temperatures of the components found in our study. [ABSTRACT FROM AUTHOR]