A function execution method and apparatus thereof for displaying one or more sub-functions included in a function selected by a first touch on a trace according to a second touch input based upon the first and the second touches inputted with a timing difference, and executing the relevant sub-function selected among the displayed one or more sub-functions. For this purpose, a function execution method according to the present invention is performed by comprising: detecting a first touch input touched on a display unit; detecting a drag created by a second touch inputted while maintaining the first touch; and displaying one or more sub-functions included in a function selected by the first touch along a trace of the detected drag on the display unit.