A differential singlemode fibre frequency-modulated continuous-wave Sagnac gyroscope is described. The gyroscope employs two Y-type fibre-optic directional couplers, two X-type fibre-optic directional couplers and a singlemode fibre coil to construct a time-division-multiplexed unbalanced fibre-optic Sagnac interferometer. The rotation velocity of the fibre coil is determined by measuring the phase difference between the two beat signals. Benefiting from the differential technique, this gyroscope can automatically eliminate the unexpected non-reciprocal phase drift (including the frequency drift of the light source) so that the accuracy and long-term stability can be significantly improved.