New polarizer and launcher systems on a 28-GHz electron-cyclotron (EC) heating and current drive (HCD) system have been developed for non-inductive second-harmonic EC-plasma-current ramp-up in the QUEST spherical tokamak. A launcher system with two quasi-optical mirrors providing beam steering capability was designed to focus the incident beam to a small-sized waist of similar to 0.05m at the second-harmonic EC resonance layer. A relatively large focusing mirror was designed based on a Kirchhoff integral code developed to derive wave solutions. The focusing property of the launched beam was first confirmed with a 3-dimensional (3D) electromagnetic-wave simulator. Focusing characteristics were also checked at low-power test facilities, together with the steering capability. The performance of this launcher system was demonstrated to work as designed, and assembled in the QUEST device. The system was applied to the non-inductive second-harmonic EC plasma ramp-up experiments with no optimization required regarding the incident polarization. The results obtained for the non-inductive plasma ramp-up are also presented.