The invention discloses a linear motor with a flexible base. The linear motor comprises a track base, a rotor base, two guide rails, more than four pulleys and a connecting shaft; the transverse section of the track base is in a concave shape; the guide rails are arranged in the outer sides of two supporting arms of the track base, and the pulleys are connected with the rotor base through the connecting shaft, and the pulleys are symmetrically arranged relative to the longitudinal cross section of the rotor base two by two; the inner sides of the two symmetrically arranged pulleys are clampedon the outer rings of the guide rails; a plurality of magnets which are arranged with interval N poles and S poles are arranged on the bottom wall of the track base in the long direction, and the bottom walls between every two adjacent magnets are made of a flexible material, so that the track base can be bent and deformed under the action of external force, so that the running line of the linearmotor can be adjusted according to the deformation of the track base.