In this paper we define a new subclass —−pseudo bi-starlike functions with respect to symmetric points of Σ related to shell-like curves connected with Fibonacci numbers and determine the initial Taylor-Maclaurin coefficients |a2| and |a3|(Formula Presnted) Further we determine the Fekete-Szeg¨o result for the function class (Formula Presented) and for special cases, corollaries are stated which some of them are new and have not been studied so far. © 2021, Kragujevac Journal of Mathematics. All Rights Reserved