We investigate the formation of the TeV spectrum of a distant blazar PKS 1424+240 residing at a redshift z >= 0.6 in two scenarios in the frame of a lepto-hadronic jet model, taking the uncertainties of both extragalactic background light (EBL) and its redshift into account. In the first scenario, TeV emission is attributed to the synchrotron emission of pair cascades resulting from the p gamma interaction. In the second scenario, TeV emission is attributed to the proton-synchrotron emission, and an internal absorption due to interaction with the photons around the jet is included. Our results show that in the first scenario the 68 per cent upper limit of its redshift, within which this scenario can explain the VERITAS TeV spectrum in 2009 well, is similar to 0.75. In the second scenario, this upper limit of the redshift becomes similar to 1.03. However, the second scenario can be excluded because it requires an unreasonable photon field around the jet with a luminosity of similar to 10(43) erg s(-1). In conclusion, the jet model can explain its TeV spectrum with a low EBL density if 0.6 < z < 0.75.