This study investigates the MTS frequency stabilisation method based on 1560 nm laser frequency doubling, optimises the analysis of the modulation transfer signal and finally locks the 1560 nm fiber laser frequency doubling to the 34 cross peak of the rubidium atom D2 line. After the laser is frequency-locked, it beats with an optical frequency comb and the standard deviation of the beat frequency value after locking for 1 h is 0.049. The Allan variance is used to characterise the performance of the system frequency locking, and the relative frequency stability after frequency locking reaches the minimum within the integration time of 10 s. The system results show that the 1560 nm fiber laser frequency locking system based on rubidium MTS can achieve excellent frequency stabilisation performance. Moreover, the frequency stabilisation system can output high-frequency stability at 1560 and 780 nm narrow-linewidth lasers simultaneously, which can be directly applied to fiber sensing, lidar and rubidium atoms as experimental media, quantum information, atomic and molecular physics and other fields.