Context.The potentially hazardous asteroid (85990) 1999 JV6 has been a target of previously published thermal-infrared observations and optical photometry. It has been identified as a promising candidate for possible Yarkovsky-O’Keefe-Radzievskii-Paddack (YORP) effect detection.Aims.The YORP effect is a small thermal-radiation torque considered to be a key factor in spin-state evolution of small Solar System bodies. In order to detect YORP on 1999 JV6 we developed a detailed shape model and analysed the spin-state using both optical and radar observations.Methods.For 1999 JV6, we collected optical photometry between 2007 and 2016. Additionally, we obtained radar echo-power spectra and imaging observations with Arecibo and Goldstone planetary radar facilities in 2015, 2016, and 2017. We combined our data with published optical photometry to develop a robust physical model.Results.We determine that the rotation pole resides at negative latitudes in an area with a 5° radius close to the south ecliptic pole. The refined sidereal rotation period is 6.536787 ± 0.000007 h. The radar images are best reproduced with a bilobed shape model. Both lobes of 1999 JV6 can be represented as oblate ellipsoids with a smaller, more spherical component resting at the end of a larger, more elongated component. While contact binaries appear to be abundant in the near-Earth population, there are only a few published shape models for asteroids in this particular configuration. By combining the radar-derived shape model with optical light curves we determine a constant-period solution that fits all available data well. Using light-curve data alone we determine an upper limit for YORP of 8.5 × 10⁻⁸rad day⁻².Conclusions.The bifurcated shape of 1999 JV6 might be a result of two ellipsoidal components gently merging with each other, or a deformation of a rubble pile with a weak-tensile-strength core due to spin-up. The physical model of 1999 JV6 presented here will enable future studies of contact binary asteroid formation and evolution.