The invention discloses a catalytic combustion engine for a high-viscosity ionic liquid propellant and a combustion method. The engine comprises a foam metal preheater, a control valve, a vortex injector, a catalytic bed, a catalytic bed preheater and an injection pipe; a porous-medium fluid channel is arranged in the foam metal preheater, the foam metal preheater is connected with one end of an inlet of the control valve, a propellant flow channel is arranged in the control valve and communicates with the porous-medium fluid channel, the other end of the control valve is connected with one end of the catalytic bed through the vortex injector, and a vortex groove is formed in the vortex injector; and the other end of the catalytic bed is connected with the injection pipe, and the catalyticbed preheater used for heating the catalytic bed is installed on the outer wall face of the catalytic bed.