By taking into account the particle's self-gravitation interaction, Hawking radiation of the uncharged and charged particles as tunneling from a Reissner-Nordstrm-anti-de Sitter black hole has been studied firstly by using the Parikh-Wilczek's semi-classical tunneling approach. Next, we generalize the complex path method to reexamine the same question. Results obtained from both methods support the viewpoint of Parikh and Wilczek's, that is, the tunneling rate is related to the change of Bekenstein-Hawking entropy, and the actual emission spectrum is not exactly thermal.