Using the effective Lagrangians formalism, we study the radiative process pp ->(gamma,Z)->nu tau nu over bar tau gamma+X in pp collisions at s=8, 13, 14, 33 TeV. Furthermore, we estimate limits at the 95% C.L. on the dipole moments of the tau-neutrino using integrated luminosities L;=20, 50, 100, 200, 500, 1000, 3000 fb(-1) collected with the ATLAS detector at the LHC and we consider systematic uncertainties delta sys=0, 5, 10%. We found that the LHC at high energy and high luminosity should provide the following limits on the anomalous magnetic and electric dipole moments of the tau-neutrino: kappa similar to nu tau=1.251x10-6 and d similar to nu tau=2.424x10-17 ecm at 95% C.L. for s=33 TeV and L =3000 fb(-1). We conclude that the process under consideration is a good prospect for probing the dipole moments of the tau-neutrino at the LHC. Our study complements other studies on the dipole moments of the tau-neutrino at pp, e+e-, gamma e- and gamma gamma colliders.