In this paper, we introduce two new classes BλΣ(m, µ) of λ-pseudo bi-starlike functions and LηΣ(m, β)to determine the bounds for|a2| and |a3 |, where a2, a3 are the initial Taylor coefficients of f ∈ BλΣ(m, µ)andf ∈ L ηΣ(m, β). Also, we attain the upper bounds of the Fekete-Szegö inequality by means of the results of |a2 | and |a3 |. © 2020 the Author(s), licensee AIMS Press.