In this paper, we introduce and investigate a new subclass Q∗∗ Σ (α, ϕ) of normalized analytic functions defined using convolution in the open unit disk U whose inverse has univalent analytic continuation to U. Estimates of the coefficients of bi-univalent functions belonging to this class are determined by using Faber polynomial techniques. © 2019 Forum-Editrice Universitaria Udinese SRL. All rights reserved.