This paper proposes extremum seeking control (ESC) schemes for Multi-functional Variable Refrigerant Flow (MFVRF) system under different operational modes, in order to maximize the efficiency provided the satisfaction of thermal comfort. Extremum seeking control is a model-free control method, which can search for unknown and time-varying optimum input(s) that can optimize a given performance index without the need for plant model. There are five operational modes considered in this study, including Cooling Only, Heating Only, Cooling Dominated, Heating Dominated, and Heat Recovery mode. For all cases, the zone temperature setpoint is achieved by controlling the respective IDU fan speed, and the feedback required is the total power consumption of the compressor motor, ODU condenser fan and IDU evaporator fans. For different operational modes, the ESC inputs are chosen to be different combinations of compressor suction pressure setpoint, ODU fan speed, bypass flow valve opening, superheat setpoints for IDU's and ODU. To evaluate the proposed control strategy, a Modelica based dynamic simulation model is developed for the multi-functional VRF system considered. Simulation results demonstrate the capability for the ESC to achieve the optimal operation in model-free fashion, as well as the potential for energy saving.