Series viscoelastic actuator (SVA), as a robot joint, can not only provide precise force estimation based on viscoelastic element, but also achieve the smooth interaction between the robot and the environment by using impedance control. Therefore, SVA is widely used in different robots in terms of rehabilitation robots, medical robots and collaboration robots. However, the viscoelastic element has the effect of strain peristalsis and stress relaxation in SVA, which results in inaccurate estimation of force and poor impedance control performance. In order to address the above issues, a combined method of force estimation and compliance control is proposed to achieve smooth interaction between the SVA and the external environments. Specifically, since Gaussian mixture model (GMM) has the advantages of large capacity and strong fitting ability, and it can fit arbitrary data through multiple Gaussian distributions. Therefore, GMM is utilized to model the relationship between rubber deformation and torque in SVA, and it realizes impedance control of SVA based on GMM torque estimation. The proposed method is verified by the experimental results.