The invention discloses a running off tracking control system and a running off tracking control method of an excavator and the excavator and belongs to the technical field of running control of the excavator. The control method comprises the following steps that firstly, a controller collects the angle value of a pedal plate and the pilot pressure value of leftward and rightward running, and the output given pressure value of a proportional valve is calculated; then, the controller collects the output pressure values of the proportional valves of a front pump and a back pump, and in addition, the output pressure values of the proportional valves of the front pump and the back pump are compared; finally, when the output pressure values of the proportional valves of the front pump and the back pump are identical, the excavator normally runs straightly; when the output pressure values of the proportional valves of the front pump and the back pump are different, the output given pressure value of the proportional valve is used as a closed ring control object, and the given current of the front pump and the back pump output by a closed ring is modified and regulated until the output pressure feedback values of the proportional valves of the front pump and the back pump are identical. The system, the method and the excavator have the advantages that the off tracking failure of the excavator is eliminated, and the comfort of operators and the work efficiency of the excavator are improved.