A shift register unit, and a shift register and a driving method thereof, are disclosed. The shift register unit includes a shift register circuit (310) and a control circuit (320). The control circuit (320) is electrically coupled to the shift register circuit (310) and at least one control terminal, and is configured, based on at least one control signal respectively from the at least one control terminal, to output a hold signal to a pull-up node in the shift register circuit (310) such that a high voltage maintains at the pull-up node during a specified time period. The shift register includes a plurality of shift register circuits cascadedly connected in stages, includes a first shift register circuit, which is coupled with a control circuit to form a shift register unit described above. The above shift register can be used in an array substrate in a display apparatus with touch control functionality.