In order to solve the problems of low integration, low reliability, and high cost caused by mechanical sensors used in bearingless permanent magnet synchronous motor (BPMSM) control systems, a novel speed and displacement sensorless control method using a least-squares support vector machine (LS-SVM) left inverse system is proposed in this paper. Firstly, the suspension force generation principle of the BPMSM is introduced, and the mathematical model of the BPMSM is derived. Secondly, the observation principle of the left inverse system is explained, and the left reversibility of the established speed and displacement subsystem is proved. Thirdly, the left inverse systems of the speed and displacement subsystems are constructed by using the LS-SVM, and the complete speed and displacement sensorless control system is constructed. Finally, the simulations and experiments of the proposed method are performed. The research results demonstrate that the proposed observation method can identify the speed and displacement quickly and accurately, and the sensorless control method can realize the stable operation of the BPMSM without speed and displacement sensors.