This study is concerned with the problem of non-fragile finite-time dissipative (FTD) control for time-varying system with delay. The delay is time varying and belongs to a given interval. Finite-time bounded (FTB) and FTD concepts are introduced to time-varying system with delay. First, new FTB conditions are derived for time-varying system with delay by using a piecewise Lyapunov functional combined with reciprocally convex approach. Second, FTD conditions are obtained to guarantee that the time-varying system with delay is not only FTB but also satisfies a dissipative performance index. Moreover, based on the FTD conditions, the non-fragile piecewise feedback controllers are designed in terms of linear matrix inequalities (LMIs). In addition, an LMI-based iterative algorithm is given to obtain the piecewise feedback non-fragile controller gains. Finally, numerical examples demonstrate the effectiveness of the proposed method.