In this paper, we consider the following equationfor p > 2 and λ > 0, which appeared in Byeon et al. (J Funct Anal 263(6):1575-1608, 2012) to find the standing wave solutions of the ChernSimons-Schrödinger system. By using the minimax theorem, we get the multiplicity results for the L 2 -normalized solutions to the equation, and thus there are multiple L 2 -normalized solutions of the Chern-SimonsSchrödinger system. Mathematics Subject Classification. 35Q55, 35A15, 35B30.