The problem of robust fault detection filter(FDF) design and optimization is studied for Markovian jump system(MJS). An observer-based residual generator is constructed and the corresponding FDF design problem is formulated as an H_∞ filtering problem. The solvable condition of the FDF and the solutions are obtained in terms of LMI. Furthermore, to improve the performance of the fault detection system, a time domain optimization approach is proposed. The solution of the optimization problem is given in the form of Moore-Penrose inverse of matrix. A numerical example is provided to show that the proposed approach has a good performance on detecting faults.