We search for a possible relation between weak gravity conjecture and conformal field theory in the hyperscaling violating and Kerr-Newman-AdS black holes. We deal with the critical points of the black hole systems through the correlation function introduced in conformal field theory. We discuss the weak gravity conjecture conditions by the imaginary part of the energy obtained from the critical points and their poles. Under the assumptions $z=1$, $d=1$ and $\theta\rightarrow0^{-}$, we link weak gravity conjecture to the hyperscaling violating black holes due to the existence of $r_{H}$ larger and smaller than one. As the second black hole system, we study the conditions of weak gravity conjecture for the Kerr-Newman-AdS black hole by rotation and radius parameters. Then, we show that the conditions of weak gravity conjecture are satisfied when the charged particle near the hyperscaling violating and Kerr-Newman black holes is $\frac{1}{a}$ with a ratio $\frac{a}{\ell}\ll 1$. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.