In this paper, the dual convolution structure for the Mehler-Fock transform is defined and obtained its estimates on Lebesgue space. Next, the two symbols σ(x, τ) and ρ(y, τ1) as an inverse Mehler-Fock transform of some measurable functions are introduced and defined the two pseudo-differential operators Pσ and Qρ respectively. Moreover, the product of two pseudo-differential operators is shown as a pseudo-differential operator. Furthermore, the boundedness of this operator in Sobolev-type space by using the dual convolution is shown and discussed the some special cases.