The problem of fault detection for linear discrete time-varying systems with multiplicative noise is dealt with. By using an observer-based robust fault detection filter (FDF) as a residual generator, the design of the FDF is formulated in the framework of H∞ filtering for a class of stochastic time-varying systems. A sufficient condition for the existence of the FDF is derived in terms of a Riccati equation. The determination of the parameter matrices of the filter is converted into a quadratic optimization problem, and an analytical solution of the parameter matrices is obtained by solving the Riccati equation. Numerical examples are given to illustrate the effectiveness of the proposed method.