Systems and methods for hoisting a top drive of a drilling rig. An example system includes a hoisting system having a linear electric motor operable to raise and lower the top drive. An example method includes commencing operation of a processing device to cause operation of the linear electric motor to raise and lower the top drive. The linear electric motor may have a stator connected to and extending vertically along a mast of the drilling rig, and a rotor connected to the top drive and operable to move relative to the stator. The rotor may be connected to the top drive via one or more flexible lines.