Liquid metal battery (LMB) is a novel battery technology that shows great application potential in the electric energy storage system. For the utilization of battery systems, an accurate estimate of the state of charge (SOC) for LMBs is of great significance. However, there are still many challenges need to be addressed due to the relatively low voltage and flat open-circuit-voltage versus SOC curve of LMBs. In this work, a novel state and parameter co-estimator is developed to concurrently estimate the state and model parameters of a Thevenin model for LMBs. The adaptive unscented Kalman filter is employed for state estimation including the battery SOC, and the forgetting factor recursive least squares is applied for online parameter estimation, which increase the model fidelity and further enhance the accuracy and robustness of the SOC estimation. A comparison with other algorithms is made based on the experimental data from laboratory-made LMBs. The evaluation results show that the proposed co-estimator exhibits the smallest root mean square error of 0.21% and is robust to external disturbances.