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In the development of tight reservoirs, the permeability of the rock possesses strong stress sensitivity with the dynamic change of formation pressure and effective stress. To quantify the stress sensitivity of permeability in tight reservoirs and its impacts on the oil production, we carried out a systematic experimental study using core samples from both tight sandstone and limestone reservoirs in Sichuan Basin. In particular, the stress sensitivity of permeability for each type of rocks was examined at reservoir conditions by two methods: (a) constant pore pressure with variable confining pressure and (b) constant confining pressure with variable pore pressure. The results show that both tight sandstone and limestone reservoirs have strong stress sensitivity of permeability, while the stress sensitivity of permeability for sandstone reservoir is larger than limestone reservoir. In addition, it is found that the variable pore pressure method can better reflect the characteristics of the stress sensitivity of permeability during the development of tight reservoirs than variable confining pressure method. The stress sensitivity of permeability for tight sandstone can be attributed to the impacts of narrow throats, while the stress sensitivity of permeability for tight limestone is dominantly influenced by the micro- and nanoscale fractures. For tight reservoirs with high stress sensitivity, the producing pressure drop can be controlled by selecting a reasonable producing pressure drop to reduce the damage in permeability caused by the stress sensitivity.