Context. Recent detections of disks around young high-mass stars support the idea of massive star formation through accretion rather than coalescence, but the detailed kinematics in the equatorial region of the disk candidates is not well known, which limits our understanding of the accretion process. Aims. This paper explores the kinematics of the gas around a young massive star with millimeter-wave interferometry to improve our understanding of the formation of massive stars though accretion. Methods. We use Plateau de Bure interferometric images to probe the environment of the nearby (∼1 kpc) and luminous (∼20 000 L ) high-mass (10-16 M ) young star AFGL 2591-VLA3 in continuum and in lines of HDO, H 18 2 O and SO 2 in the 115 and 230 GHz bands. Radiative transfer calculations are employed to investigate the kinematics of the source. Results. At ∼0.5 (500 AU) resolution, the line images clearly resolve the velocity field of the central compact source (diameter of ∼800 AU) and show linear velocity gradients in the northeast-southwest direction. Judging from the disk-outflow geometry, the observed velocity gradient results from rotation and radial expansion in the equatorial region of VLA3. Radiative transfer calculations suggest that the velocity field is consistent with sub-Keplerian rotation plus Hubble-law like expansion. The line profiles of the observed molecules suggest a layered structure, with HDO emission arising from the disk mid-plane, H 18 2 O from the warm mid-layer, and SO 2 from the upper disk. Conclusions. We propose AFGL 2591-VLA3 as a new massive disk candidate, with peculiar kinematics. The rotation of this disk is sub-Keplerian, probably due to magnetic braking, while the stellar wind may be responsible for the expansion of the disk. The expansion motion may also be an indirect evidence of disk accretion in the very inner region because of the conservation of angular momentum. The sub-Keplerian rotation discovered in our work suggests that AFGL 2591-VLA3 may be a special case linking transition of velocity field of massive disks from pure Keplerian rotation to solid-body rotation though definitely more new detections of circumstellar disks around high-mass YSOs are required to examine this hypothesis. Our results support the idea that early B-type stars could be formed with a circumstellar disk from the point of view of the disk-outflow geometry, though the accretion processes in the disk need to be further investigated.