The fusion estimation problem for a class of multi-sensor asynchronous sampling linear stochastic systems with missing measurements is considered, where the state is updated uniformly and each sensor non-uniformly samples one measurement at most within a state update period. Based on the sampled measurement data of each sensor, the optimal local state estimators are designed at the state and measurement points by using the projection theory. The cross-covariance matrices between estimation errors of any two local estimators are derived. Based on the obtained local estimators and cross-covariance matrices, the distributed optimal fusion estimator is given by using matrix-weighted fusion estimation algorithm in the linear minimum variance sense. A simulation example verifies the effectiveness of the algorithms.