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This paper deals with the derivation of the Kober fractional q-integral operator of the basic analogue of the H-function defined by Saxena, Modi and Kalla [Rev. Téc. Ing., Univ. Zulia. 6(1983), 139-143]. Several interesting results involving Gq(.);Eq(.); the basic elementary functions and the basic Bessel functions such as Jv(x; q); Yv(x; q); Kv(x; q); Hv(x; q), are deduced as the special cases of the main results.