The characteristics of nanogratings including damage trace, structure and birefringence properties, which are induced in fused silica by 1 kHz femtosecond laser pulses with different pulse energy, are studied. Two different periodic nanostructures are observed at the top of laser irradiation area, the primary structure with the period ΛK in the direction of light propagation and the secondary structure with the period ΛE in the direction of laser beam polarization. The influence of incident energy flux density distribution and free electron density distribution on doubly-periodic nanogratings is investigated by numerically simulating the propagation process of femtosecond laser pulses inside the fused silica. The results show that higher incident energy flux density benefits the formation of nanogratings, and the generated electron density influences the period ΛK. The higher the electron density is, the longer the period ΛK is. The formation of doubly-periodic nanogratings is analyzed theoretically according to current experimental results. The asymmetric growth of plasma and the causing local intensity distribution affect the formation of doubly-periodic nanogratings.