Based on the W∞ symmetry of the q-deformed Kadomtsev-Petviashvili (q-KP) hierarchy,which is a q-deformation of the KP hierarchy,we construct the quantum torus symmetry of the q-KP hierarchy,which further leads to the quantum torus constraint of its tau function.Moreover,we generalize the system to a multi-component q-KP hierarchy that also has the well-known ghost symmetry.