In this study, we investigate the effect of uniaxial strain on the thermal conductivity of zigzag graphene (ZG) and armchair graphene (AG). It is observed that the thermal conductivity reduces with strain in ZG and AG. For a given strain, the maximum reduction in thermal conductivity is observed in AG. The tensile strain causes a larger deformation of bonds in AG whereas a minor variation in bond angles is observed. This causes a high reduction of thermal conductivity in AG. DOS (Density of States) and Spectral Energy Density (SED) curves are calculated to study the phonon transport in graphene. It is found that due to strain, high frequency phonon modes undergo a red shift whereas blue shift is observed in the out-of-plane phonon modes. The phonon group velocity and lifetimes of in-plane acoustic modes get reduced because of strain and hence their contribution to the thermal conductivity reduces. But in the ZA modes, strain increases the phonon group velocities and phonon lifetimes. For unstrained graphene, in-plane acoustic modes contribute nearly 60-70% of thermal conductivity in ZG and AG. However, when graphene is strained their contribution sharply reduces and the contribution by ZA mode increases and is nearly 40-60% of the thermal conductivity. But the contribution by TA modes to the thermal conductivity is unaffected by strain. Phonon Mean Free Path (MFP) calculations indicate that MFP of phonon in strained graphene increases due to increase in the wavelength of low frequency ZA phonons. The MFP of phonons is found to be higher in AG than in ZG in both strained and unstrained conditions. © 2019, Avestia Publishing.