In this paper we define a new subclass $\lambda-$pseudo bi-starlike functions with respect to symmetric points of $\Sigma$ related to shell-like curves connected with Fibonacci numbers and determine the initial Taylor-Maclaurin coefficients $|a_2|$ and $|a_3|$ for $f\in\mathcal{PSL}^\lambda_{s,\Sigma}(\alpha,\tilde{p}(z)).$ Further we determine the Fekete-Szeg$\ddot{o}$ result for the function class $\mathcal{PSL}^\lambda_{s,\Sigma}(\alpha,\tilde{p}(z))$ and for special cases, corollaries are stated which some of them are new and have not been studied so far.