Classical molecular dynamics(MD) simulations are performed to investigate the effects of mechanical strain on the thermal conductivity of single-layer black phosphorus(SLBP) nanoribbons along different directions at room temperature. The results show that the tensile strain affects the thermal conductivity of nanoribbons by changing the phonon density of state (DOS) and mean free path (MFP). The thermal conductivity shows a sharp enhancement with the tensile strain applied along the armchair direction, while it increases slowly with the strain applied along the zigzag direction. This phenomenon can be mainly explained by effects of the phonon DOS and MFP. The increasing strain along the armchair direction weakens DOS and strengthens MFP clearly. However, when it comes to the increasing strain along the zigzag direction, DOS enhances significantly while MFP decreases slightly. The findings explore the relationship between the tensile strain and the thermal conductivity reasonably and can provide a reliable method to estimate the MFP of black phosphorus.