Single-layer MoS2 (SLMoS2) nanosheets promise potential applications in flexible electronic and optoelectronic nanodevices for which the mechanical stability is crucial. However, the measured fracture strength is extremely dispersive, which might be due to the random crack configuration. In this work, molecular dynamics (MD) simulations are conducted to investigate the propagation of nanocracks in SLMoS2 nanosheets and the fracture mechanism at atomic scale, and the modified Griffith criterion developed by Yin et al. is adopted to fit the dependence of fracture stress on the initial crack length. Moreover, the fracture stress is highly dependent on the initial crack configuration, crack length, and crack angle. The energy release rate (G(s)) decreases with increasing initial crack length, crack angle, and temperature but is not sensitive to strain rate. The average propagation velocity of cracks (V) is substantially reduced with increasing initial crack length and crack angle but is almost independent of temperature and strain rate. The V at lower G(s) is well predicted by linear elastodynamic theory but approaches 66% Rayleigh-wave speed at a higher Gs of >5.78 J/m(2). It is also found that fracture is preferred along the zigzag direction of SLMoS2 nanosheets. The results provide us a clear understanding on the dispersive data of measured fracture strength of SLMoS2 nanosheets.