Stimulated Raman scattering microscopy allows label-free chemical imaging and has enabled exciting applications in biology, material science and medicine. It provides a major advantage in imaging speed over spontaneous Raman scattering and has improved image contrast and spectral fidelity compared to coherent anti-Stokes Raman scattering. Wider adoption of the technique has, however, been hindered by the need for a costly and environmentally sensitive tunable ultrafast dual-wavelength source. We present the development of an optimized all-fibre laser system based on the optical synchronization of two picosecond power amplifiers. To circumvent the high-frequency laser noise intrinsic to amplified fibre lasers, we have further developed a high-speed noise cancellation system based on voltage-subtraction autobalanced detection. We demonstrate uncompromised imaging performance of our fibre-laser-based stimulated Raman scattering microscope with shot-noise-limited sensitivity and an imaging speed up to 1 frame s-1.