This paper investigates the strategies for adopting blockchain technology in the fresh product supply chain (FPSC) consisting of a supplier, a third-party logistics service provider (3PL) and an e-tailer. We analyse the optimal strategies of FPSC members under the benchmark scenario where the FPSC does not adopt blockchain technology and those under the three scenarios where the supplier, 3PL and e-tailer lead the construction of the blockchain-based traceability system (BTS), respectively. We find that adopting blockchain technology is not always the optimal decision for the FPSC, which is related to the consumers' acceptance degree for the product without blockchain technology, the deterioration rate of the fresh product and the allocation proportion of traceability cost of FPSC members when adopting blockchain technology. Regardless of the power and status of each member in the FPSC, it can lead the construction of the BTS. From the perspective of whole FPSC's profit maximisation, the leader of the FPSC should lead the construction of the BTS under the coordination of a two-part tariff contract. This study provides valuable insights for FPSCs to adopt blockchain technology.