In this paper we define the subclass \(\mathcal{PSL}^\lambda_{s,\Sigma}(\alpha,\tilde{p}(z))\) of the class \(\Sigma\) of bi-univalent functions defined in the unit disk, called \(\lambda\)-bi-pseudo-starlike, with respect to symmetric points, related to shell-like curves connected with Fibonacci numbers. We determine the initial Taylor-Maclaurin coefficients \(|a_2|\) and \(|a_3|\) for functions \(f\in\mathcal{PSL}^\lambda_{s,\Sigma}(\alpha,\tilde{p}(z)).\) Further we determine the Fekete-Szegö result for the function class \(\mathcal{PSL}^\lambda_{s,\Sigma}(\alpha,\tilde{p}(z))\) and for the special cases \(\alpha=0\), \(\alpha=1\) and \(\tau =-0.618\) we state corollaries improving the initial Taylor-Maclaurin coefficients \(|a_2|\) and \(|a_3|\).