Microbunching instability usually exists in the linear accelerator （linac） of a free electron laser （FEL） facility. If it is not controlled effectively, the beam quality will be damaged seriously and the machine will not operate properly. In the electron linac of a soft X-ray FEL device, because the eiectron energy is not very high, the problem can become even more serious. As a typical example, the microbunching instability in the linac of the proposed Shanghai Soft X-ray Free Electron Laser facility （SXFEL） is investigated in detail by means of both analytical formulae and simulation tools. In the study, a new mechanism introducing random noise into the beam current profile as the beam passes through a chicane-type bunch compressor is proposed. The higher-order modes that appear in the simulations suggest that further improvement of the current theoretical model of the instability is needed.