The electronic and optical properties of XPdBi (X = Lu, Sc) nano-layers are investigated in the framework of first principles density functional theory by Wien2k code. The exchange-correlation potential is calculated within the generalized gradient approximation and Engel-Vosco generalized gradient approximation. The effect of nano layer thickness on the electron density of states, energy gap and topological phase of these nano-layers is studied and compared. The surface states of LuPdBi nano-layers undergo a topological phase transition with increasing the thickness. The charge density of XPdBi nano-layers surface atoms with two different thicknesses is investigated. The results show the ionic bonding between X and Bi surface atoms of these nano-layers. The electric field gradient and the interaction of electronic orbital wave functions with the electronic cloud distribution of these nano layers surface atoms with different thicknesses are calculated and compared. The anisotropic optical response of these nano-layers to two electromagnetic waves polarizations is investigated. Furthermore, the effect of nano layer thickness on the optical properties of these nano-layers is studied in the 0-35 eV energy range. (C) 2016 Published by Elsevier B.V.