A non-coated woven fabric for air bag according to the present invention comprises a synthetic fiber containing 90% by weight or more of Nylon 66, characterized in that crimping rate of warp of the fabric is 10.0 to 13.0% while crimping rate of woof of the fabric is 6.0% or less, relative viscosity of Nylon 66 constituting the synthetic fiber in sulfuric acid is 3.15 to 3.7, the synthetic fiber contains 40 ppm to 200 ppm of phosphorus component and, when dynamic air permeability of the fabric is measured at a maximum pressure of 80±5 kPa based on ASTM D 6476 under the environment of 20° C.×65% RH, biaxial elongation strain hysteresis of the fabric during a transition from increased pressure to reduced pressure at 50 kPa is 0.69% to 1.0%.