Consumer impulsive purchasing is very common, especially in the livestream selling where they are influenced by policies such as low prices, limited time, and limited quantity. This behavior can increase a firm's sales, but it also leads to higher return rates. Considering consumer impulse purchase, this paper conducts an analytical model to investigate the conditions for a firm to introduce a livestream channel and whether the firm should adopt a low or moderate livestream price strategy when introducing a livestream channel. Our results show that, when return processing cost is small enough, the firm benefits from the livestream strategies as long as the streamer's fan effect is larger than a threshold. Specifically, a firm prefers to adopt the low livestream price strategy when cooperating with a large fan effect streamer and a moderate livestream price strategy with a small fan effect streamer. However, when return processing cost is large, the low livestream price strategy cannot be the dominant strategy. Furthermore, we make several extensions (i.e., different impulse utility on different livestream price, impact of positive impulse utility of low impulsive consumers, different online return rates of different types of consumers, the costs of introducing the livestream channel, and consumer return processing cost) to verify the robustness of the model, and the main conclusions remain unchanged. These results provide guidance for firms on the introduction of livestream channel and pricing decisions of different channels.