  We study the stellar kinematic properties and spatial distribution of the
association Cyg OB3 using precise astrometric data from Gaia DR2. All known O-
and B-type stars in Cyg OB3 region with positions, parallaxes and proper
motions available are included, comprising a total of 41 stars. The majority of
stars are found to be concentrated at a heliocentric distance of 2.0 +/- 0.3
kpc. The mean peculiar velocity of the sample after removing Galactic rotation
and solar motion is ~22 km/s, dominated by the velocity component towards the
Galactic center. The relative position and velocity of the black hole X-ray
binary Cyg X-1 with respect to the association suggest that Cyg OB3 is most
likely its parent association. The peculiar kinematic properties of some of the
stars are revealed and are suggestive of past stellar encounters. The sample
includes a previously known runaway star HD 227018, and its high peculiar
velocity of ~50 km/s is confirmed with Gaia. We estimated the velocities of
stars relative to the association and the star HD 225577 exhibits peculiar
velocity smaller than its velocity relative to the association. The star has
lower value of proper motion than the rest of the sample. The results suggest a
slowly expanding nature of the association, which is supported by the small
relative speeds <20 km/s with respect to the association for a majority of the
sample stars.
