A new recursive method for obtaining the mean waiting time in a polling system with general service order and gated service discipline is proposed. The analytical approach used to obtain the mean waiting time is via an imbedded Markov chain and a new recursive method is used to obtain the moments of pseudocycle time which are parameters in the formula for the mean waiting time. This method is computationally tractable, so the analytical results can cover a wide range of applications. Simulations are also conducted to verify the validity of the analysis.