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We deal with the problem of distributed fusion estimation for multi-sensor sampled systems where a kind of typical faults may occur. Firstly, the innovation obtained from Kalman filter is used for fault detection of local sensor. Then an online recursive sensor fault estimation scheme is developed in the sense of minimum variance. Furthermore, using the estimation result to reconstruct the measurement of the faulty sensor, a fault tolerant update algorithm is built with help of projection theory. Based on the linear minimum variance criterion, a distributed fault tolerant estimation scheme is finally developed for multi-sensor sampled systems. Comparing with the existing method, the proposed scheme can not only detect faults in time, but also make full use of information of the faulty sensor to improve the overall estimation accuracy. Simulation results demonstrate the effectiveness and superiority.