We study almost periodic pseudodifferential operators acting on almost periodic functions G s ap (R d )  of Gevrey regularity index s ≥ 1. We prove that almost periodic operators with symbols of Hörmander type S m ρ,δ   satisfying an s-Gevrey condition are continuous on G s ap (R d )  provided 0 < ρ ≤ 1, δ = 0 and s ρ ≥ 1. A calculus is developed for symbols and operators using a notion of regularizing operator adapted to almost periodic Gevrey functions and its duality. We apply the results to show a regularity result in this context for a class of hypoelliptic operators.