A broadcast processing apparatus which has a time shift function, includes: a buffer unit which buffers a broadcast signal; a selection unit which is provided to select a broadcast signal recording function; a storage unit; a user interface (UI) generator which generates UI information; a display unit; and a controller which controls the UI generator to display the UI information on the display unit and select a recording range of the buffered broadcast signal and records the broadcast signal corresponding to the selected recording range in the storage unit if the broadcast signal recording function is selected.