As a novel sales strategy, live-streamed selling has drawn considerable interest. In this paper, we study a dual-channel live-streaming supply chain consisted of a single manufacturer, a moderate live streamer and a live-streaming platform. We construct two scenarios, the retail live streaming and commissioned live streaming modes, under manufacturer self-live streaming and investigates the optimal mode with the Stackelberg games. The study discovers: (1) Under the commissioned live streaming mode, the price of Internet celebrity live streaming is less expensive than that under manufacturer self-live streaming within a specific commission ratio and is proportionate to the commission ratio. (2) Under the retail live streaming mode, only when consumers' preferences are more concentrated on the manufacturer self-live streaming, the price of Internet celebrity live streaming is less than the manufacturer self-live stream channel. (3) In both scenarios, Internet celebrity live-streaming sales effort is consistently lower than the manufacturer self-live stream channel. Additionally, the consumer's sensitivity coefficient and the trust degree in Internet-celebrity streamer, the personal impact of Internet-celebrity streamer, and the proportion of impulsive consumers are all positively correlated with the price, sales effort, and profit of both channels.