A novel flow reactor packed with a fibrous catalytic cloth is proposed to carry out a gas-liquid reaction. Radial flow and separation of the transport of the gaseous reactant and the reaction are the main features of the new design. An activated carbon cloth supported 2 wt % Pd-0.6 wt % Cu bimetallic catalyst installed in the reactor was applied for the water-phase nitrate hydrogenation, showing selectivity up to 84% toward nitrogen at a nitrate conversion of up to 93%. The reactor performance has been evaluated using the diagnostic criteria associated with varying the hydrogen pressure, liquid flow rate, and catalyst loading in the reactor; it was described by a simplistic model, assuming one-dimensional, plug-flow, and steady-state operation. The significance of mass-transfer effects on the reactor performance has been analyzed. The results obtained indicate that the reactor investigated has a high potential for further development and scale-up.