A method of sharing a screen of a first device with a second device and a device using the same are provided. The method includes transmitting information on a first screen displayed on the first device to the second device, in a first connection state so that a same screen is displayed by the first device and the second device; switching the first connection state between the first device and the second device into a second connection state; and performing a control so that the first screen displayed on the first device is switched into a second screen so that the first screen displayed is continuously displayed on the second device, when a user input is received in a state in which the first connection state is switched into the second connection state in which an independent screen is displayed by the first device and the second device.