This paper proposes a novel hybrid active power filter (HAPF) topology based onthe cascaded connection of the AC-side capacitor and the third-order LCL-filter, which hasthe advantage of the conventional hybrid filter and the LCL-filter in terms of reduced dclinkvoltage and better switching ripple attenuation. The robust deadbeat control law isderived for the current loop, with special emphasis on robustness analysis. The stabilityand robustness analysis under parameter variations are presented for the converter-sidecurrent tracking scheme and the grid-side current tracking scheme. It is found that thestability margins obtained from the converter-side current tracking control scheme aregenerally higher than those obtained from the grid-side current tracking scheme. However,the converter-side current tracking scheme is sensitive to the variation of the dampingresistance, and it would impose additional parameter uncertainty on the control system andcomplicate the problem. Hence the grid-side current tracking scheme is implemented. Thesimulation results obtained from Matlab/Simulink are presented for verification, where theinductance variation and grid disturbance scenarios are also taken into consideration. Theeffectiveness of the proposed hybrid APF is substantially confirmed by the simulation andexperimental results.