In this paper, we consider the following quasilinear Schrödinger–Poisson system with exponential and logarithmic nonlinearities where are parameters, is a bounded domain, and has exponential critical growth. By adopting the reduction argument and a truncation technique, we prove for every , the above system admits at least one pair of nonnegative solutions for large. Furthermore, we research the asymptotical behavior of solutions with respect to the parameters and . The novelty of this system is the intersection among the quasilinear term, logarithmic term, and exponential critical term. These results are new and improve some existing results in the literature.