This paper proposes a bias fault estimation method by a single observer, which is based on the compress sensing. Fault-tolerant control of systems becomes increasingly important to keep safety of systems. The bias fault estimation is one of the most important technologies in fault-tolerant control theory, especially for passive fault-tolerant servo systems. For the bias fault estimation problem, the disturbance observer approach has been proposed. However, this approach cannot be applied to the estimation of all faults at both actuators and sensors by a single observer. In this paper, a bias fault estimation method based on the compress sensing is proposed. Under the assumption that only one device fault occurs at a time, the bias fault estimation method by a single observer can be formulated as an optimization problem with l0 norm constraint. This paper gives a numerical example to demonstrate the effectiveness of the proposed estimation method.