The paper deals with the Cauchy problem of Navier-Stokes-Nernst-Planck-Poisson system (NSNPP). First of all, based on so-called Gevrey regularity estimates, which is motivated by the works of Foias and Temam [J. Funct. Anal., 87 (1989), 359-369], we prove that the solutions are analytic in a Gevrey class of functions. As a consequence of Gevrey estimates, we particularly obtain higher-order derivatives of solutions in Besov and Lebesgue spaces. Finally, we prove that there exists a positive constant \begin{document}$\mathbb{C}$\end{document} such that if the initial data \begin{document}$(u_{0}, n_{0}, c_{0})=(u_{0}^{h}, u_{0}^{3}, n_{0}, c_{0})$\end{document} satisfies \begin{document}$\begin{aligned}&\|(n_{0}, c_{0},u_{0}^{h})\|_{\dot{B}^{-2+3/q}_{q, 1}× \dot{B}^{-2+3/q}_{q, 1}×\dot{B}^{-1+3/p}_{p, 1}}+\|u_{0}^{h}\|_{\dot{B}^{-1+3/p}_{p, 1}}^{α}\|u_{0}^{3}\|_{\dot{B}^{-1+3/p}_{p, 1}}^{1-α}≤q1/\mathbb{C}\end{aligned}$ \end{document} for \begin{document}$p, q, α$\end{document} with \begin{document}$1 \frac{1}{3}, 1 , then global existence of solutions with large initial vertical velocity component is established.