The thermal conductivity of monolayer graphene nanoribbons (GNRs) with different tensile strain is investigated by using a nonequilibrium molecular dynamics method. Significant increasing amplitude of the molecular thermal vibration, molecular potential energy vibration and thermal conductivity vibration of stretching GNRs were detected. Some 20%~30% thermal conductivity decay is found in 9%~15% tensile strain of GNR cases. It is explained by the fact that GNR structural ridges scatter some low-frequency phonons which pass in the direction perpendicular to the direction of GNR stretching which was indicated by a phonon density of state investigation.