In this paper we study the following zero mass Schrödinger-Bopp-Podolsky system with critical growth: \(\begin{aligned} \begin{array}{ll} \displaystyle \left\{ \begin{array}{ll} \displaystyle -\Delta u+q^2\phi u=\mu |u|^{p-2}u+|u|^{4}u,\quad & x\in \mathbb {R}^3,\\ -\Delta \phi +a^2\Delta ^2\phi =4\pi u^2,\quad & x\in \mathbb {R}^3, \end{array} \right. \end{array} \end{aligned}\) where \(a>0\) , \(q\ne 0\) , \(\mu >0\) is a parameter and \(p\in (3,6)\) . By introducing a new functional framework developed by Caponio et al. [9], we first establish the existence of positive ground state solutions for the case of \(p\in (3,6)\) . Moreover, for the case of \(p\in (4,6)\) , multiplicity results are obtained by applying an abstract critical point theorem due to Perera [31].
