The present paper describes the current baseline optical design of POLLUX, a high-resolution spectropolarimeter for the future LUVOIR mission. The instrument will operate in the ultraviolet (UV) domain from 90 to 390 nm in both spectropolarimetric and pure spectroscopic modes. The working range is split between 3 channels-far (90-124.5 nm), medium (118.5-195 nm) and near (195-390 nm) UV. Each of the channels is composed of a polarimeter followed by an echelle spectrograph consisting of a classical off-axis paraboloid collimator, echelle grating with a high grooves frequency and a cross-disperser grating operating also as a camera. The latter component integrates some advanced technologies: it is a blazed grating with a complex grooves pattern formed by holographic recording, which is manufactured on a freeform surface. One of the key features underlying the current design is the large spectral length of each order ~6 nm, which allows to record wide spectral lines without any discontinuities. The modelling results show that the optical design will provide the required spectral resolving power higher than R ~ 120,000 over the entire working range for a point source object with angular size of 30 mas. It is also shown that with the 15-m primary mirror of the LUVOIR telescope the instrument will provide an effective collecting area up to 38 569 cm 2. Such a performance will allow to perform a number of groundbreaking scientific observations. Finally, the future work and the technological risks of the design are discussed in details.