A new nanodosimetry-based cell survival model for mixed high- and low-LET radiations has been developed. The new model employs three dosimetry quantities and three biological quantities. The three dosimetry quantities are related to energy depositions at two nanometer scales, 5nm and 25nm. The three biological quantities are related to lesion production and interaction probabilities, and lesion repair rate. The model assumes that the lesions created at the two nanometer scales are directly or indirectly responsible for cell death depending on the lesions interaction and repair rate. The cell survival fraction derived from the new model can be expressed by the familiar dose-dependent linear quadratic formula. The coefficients alpha and beta are based on the three nanodosimetry quantities and the three biological quantities. Validation of the new model has been performed both by using published data and by the experimental data obtained. Published cell survival curves for V-79 Chinese hamster cells irradiated with various LET of radiations were used for validation. The new model was applied to radiation therapy by irradiating V-79 cells with mixed fission neutron and gamma-rays. The results show that the new model has been successfully used in a mixed n+g field to predict the synergistic effect between neutron and gamma-ray lesions and the RBE for fission neutrons.