The fractional q-calculus is the q-extension of the ordinary fractional calculus.In the second half of the twentieth century there was a significant increase of activity in the area of the q-calculus due to its applications in mathematics and physics.Particularly, the operators of fractional calculus and their q-analogues have many applications.They can be used in crack problems in elasticity, in chaos theory, control systems, signal processing, bio-medical engineering, radars, sonars, etc.The aim of this paper is to define a new fractional q-integral operator of Kober type using the basic analogue of Fox-Wright function as kernel, and to establish a composition formula for a particular type of these operators.Also, some particular cases are obtained.