A livestreaming supply chain composed of a single manufacturer and a single streamer in the low-carbon market is examined. Motivated by the actual production and operation, both the manufacturer and the streamer have a chance to dominate the supply chain. Low-carbon strategies and livestreaming marketing modes of the supply chain are studied. The impacts of the consumer’s price sensitivity coefficient, low-carbon preference, and streamer’s promotion sensitivity coefficient on the equilibrium results are further studied. The results show that: the streamer achieves the optimal level of promotion effort in the resale mode under both power structures. The manufacturer achieves the optimal low-carbon level in the commission mode when the promotion sensitivity coefficient is smaller under both of two power structures. The streamer’s profit is optimal in the resale mode, while the manufacturer’s profit is optimal in the commission mode when under the streamer-led structure. Two parties’ profits are optimal in the commission mode when the promotion sensitivity coefficient is smaller under the manufacturer-led structure. The low-carbon level, streamer promotion effort and selling price in two livestreaming marketing modes will increase when the streamer promotion sensitivity coefficient and consumer low-carbon preference increase and will decrease when consumer price sensitivity increases under two power structures. Lastly, the selling price in resale mode is always higher than that in commission mode under two power structures.