The widespread application of outsourced computation meets the growing computing demands. However, due to the payment issues and data security, achieving fair interaction between clients and workers in a zero-trust environment has become a bottleneck of restricting the development of outsourced computation. Most existing solutions, including blockchain-based and traditional e-cash system, may compromise the client's or the worker's fairness. To deal with this issue, several fair payment schemes based on trusted third parties (TTP) have been proposed in the literature. However, the involvement of TTP reduced the feasibility of these schemes. In order to remove the aforementioned limitations, we propose a lightweight bitcoin-based fair payment (LBFP) scheme for outsourced computation environment. LBFP is able to achieve the robust fairness and compatibility by integrating cryptographic components (including one-way accumulator, bitcoin-based timed commitment, and symmetric encryption). In addition, we give the security analysis of LBFP and make a comparison with the related schemes which show that LBFP has a better application prospect.