We present a conceptual proposal for a large-orbit coaxial-structure cyclotron autoresonance maser (CARM), wherein the rf structure is a coaxial waveguide or cavity and a large-orbit electron beam encircles the axis of the coaxial structure. Both dispersion analysis and nonlinear simulations demonstrate the feasibility of the proposal. The large-orbit coaxial-structure CARM could be expected to operate in millimeter and submillimeter wave ranges with high power, low operating magnetic field, and ultrahigh gain. It is found that electron-beam velocity spread substantially decreases the power of CARMs, but this adverse influence might be offset by a proper taper of the axial magnetic field.