Quantum digital signature (QDS) can guarantee message integrity and non-repudiation with information-theoretical security, and it has attracted more attention recently. Since proposed by Andersson et al. [Phys. Rev. A93, 032325 (2016)PLRAAN1050-294710.1103/PhysRevA.93.032325], a quantum digital signature protocol using an insecure channel has been realized with several different quantum key distribution (QKD) systems. Here we report an experimental QDS based on a BB84 QKD system. An asymmetric Faraday-Sagnac-Michelson interferometer structure has been designed in our system, which is intrinsically stable against channel disturbance. The innovatory structure supports the system to work at high speed and, in practice, the repetition rate is in gigahertz. A 0.044 bit/s signature rate has been attained with a 25 dB channel loss composed of a 25 km installed fiber with additional optical attenuation in a 10-10 security level. Thus, our QDS device is stable and highly efficient. This Letter provides a further step for the practical application of QDS.