As a new trend of the e-commerce market, live streaming e-commerce is attracting more and more attention. Quality effort strategies of a live streaming e-commerce service supply chain containing a brand service provider, a streamer and a live streaming service platform are researched. By analyzing the two situations of whether the streamer signs contracts with the platform, we establish members' profit functions respectively. Meanwhile, with the goal of profit maximization, the optimal quality effort strategy and profits of the supply chain members are obtained by using the game theory. Through numerical simulation, we discuss the effects of the streamer commission proportion and proportion of live service platform on the optimal strategies and profits of the service supply chain. We can get the conclusions: in the two cases, the optimal service quality efforts of the streamer increase with the increase of the streamer commission proportion and decrease with the proportion of the live streaming service platform; but the optimal service quality efforts of the live streaming service platform increase with the increase of the streamer commission proportion and the proportion of the live streaming service platform.