A home appliance, a mobile terminal, and an operation method thereof are disclosed. The home appliance includes a communication unit to receive a remote control signal from a mobile terminal, an input unit to receive a user input signal from a local key, and a controller to assign priority to the user input signal according to the input of the local key and to control an operation of the home appliance corresponding to the user input signal when a time difference between input of the local key and reception of the remote control signal is within a predetermined time. When a plurality of control rights is requested, the home appliance may assign priority to any one of the requested control rights.