We propose a procedure to manipulate the chirality and propagation of a vortex domain wall in ferromagnetic nanotubes by applying magnetic field pulses. It is found that the chiral state of the vortex wall can be switched, provided that (1) the field amplitude is between two critical values, the so-called chiral field and the well-known Walker field, and (2) the pulse length is longer than a critical time, which is the time needed by the wall to overcome a local energy barrier. These key parameters are estimated for Permalloy nanotubes and range between a few miliTesla and some nanoseconds.