This paper is concerned with the ergodic stochastic optimal control problem with Markov Regime-Switching in a dissipative system. The proposed approach primarily relies on duality techniques. The control system is described by controlled dissipative stochastic differential equations and modulated by a continuous-time, finite-state Markov chain. The cost functional is ergodic, which is the expected long-run mean average type. The control domain is assumed to be convex, and the convex variation technique is used. Both necessary condition version and sufficient condition version of the stochastic maximum principle are established for optimal control. An example is discussed to illustrate the significance of our results.