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 \pm 0.3 kpc .
The mean peculiar velocity of the sample after removing Galactic rotation and solar motion is \sim 22 km s ^ { -1 } , 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 \sim 50 km s ^ { -1 } 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 ^ { -1 } with respect to the association for a majority of the sample stars .