The random distributed-feedback fiber laser (RFL) is a new approach to obtain a high-power stable supercontinuum (SC) source. To consider both structure simplification and high-power SC output, an innovative structure achieving a kilowatt-level SC output in a single-stage RFL with a half-open cavity is demonstrated in this paper. It consists of a fiber oscillator, a piece of long passive fiber and a broadband coupler, among which the broadband coupler acting as a feedback device is crucial in SC generation. When the system has no feedback, the backward output power is up to 298 W under the pump power of 1185 W. When the feedback is introduced before the pump laser, the backward power loss can be reduced and the pump can be fully utilized, which could promote forward output power and conversion efficiency significantly. Under the maximum pump power of 1847 W, a 1300 W SC with spectrum ranging from 887 to 1920 nm and SC conversion efficiency of 66% is obtained. To the best of our knowledge, it is the simplest structure used for high-power SC generation, and both the generated SC output power and the conversion efficiency are highest in the scheme of the half-opened RFL output SC.