We demonstrate an efficient method for far-field subwavelength focusing by a novel two-component axicon structure. Annular beams generated by a fiber axicon are focused using a micro-cone reflector, creating a quasi-Bessel beam with a high convergence angle of up to 40°. A center focal spot diameter of 0.41λ was achieved at a power efficiency of over 40%, with a focal depth of 9λ and a working distance as long as 35 μm. We further demonstrate that experimental knife-edge measurements mapping the beam focal intensity agree with numerical simulations of the structure. This method shows demonstrable promise in overcoming the optical focusing limit of single-element axicons and great potential for use in high tolerance, high-resolution applications in optical systems.