Gauge boson self-couplings are exactly determined by the non-Abelian gauge nature of the Standard Model (SM), thus precision measurements of these couplings at the LHC providean important opportunity to test the gauge structure of the SM and the spontaneoussymmetry breaking mechanism. It is a common way to examine the physics of anomalous quartic gauge boson couplings via effective Lagrangian method. In this work, we investigate the potential of the process pp -> p gamma p -> pWZqX to analyze anomalous quartic WWZ gamma couplings by two different, CP- violating and CP-conserving, effective Lagrangians at the LHC. We calculate 95% confidence level limits on the anomalous coupling parameters with various values of the integrated luminosity. Our numerical results show that the best limits obtained on the anomalous couplings k(0)(W)/A(2), k(W)c/A(2), k(2)(m)/A(2) and a(n)/A(2) at root s = 14 TeV and an integrated luminosity of L-int = 100fb(-1) are [-1.37; 1.37] x10(-6) GeV-2, [-1.88; 1.88] x10(-6) GeV-2, [-6.55; 6.55] x10(-7) GeV-2 and [-2.21; 2.21] x10(-6) GeV-2, respectively. Thus, gamma p mode of photon-induced reactions at the LHC highly improves the sensitivity limits of the anomalous coupling parameters k(0)(W)/A(2), k(W)c/A(2), k(2)(m)/A(2) and a(n)/A(2) . (C) 2015 The Authors. Published by Elsevier B.V.