The present application discloses a multi-split air conditioner and a control method thereof. The multi-split air conditioner includes a plurality of outdoor heat exchangers connected in parallel to a refrigerant main circulation passage, wherein a parallel branch in which each of the plurality of outdoor heat exchangers is located is provided with a branch control valve capable of controlling a flow rate of refrigerant flowing through the parallel branch. The control method includes: determining a current superheat degree of the multi-split air conditioner; when the current superheat degree of the multi-split air conditioner deviates from a set target superheat degree, controlling and regulating the flow rate of the refrigerant flowing through the branch control valve; and controlling and regulating the flow rate of the refrigerant flowing through the air supplement control valve according to the flow rate of the refrigerant flowing through each of branch control valves.