In this work, we will present detailed calculations to derive the exact formulas of the triple and quartic self-couplings of all gauge bosons predicted by the general 3-3-1 model with an arbitrary parameter β used to classify different 3-3-1 models. We show that our result is consistent with all previous results calculated for particular β values. The respective Feynman rules are introduced for further studies on physical processes relating to these gauge bosons.