Weather condition is an important factor affecting the air transportation, and it is essential for improving the air transportation capacity to identify the resilience recovery mechanism of civil airport infrastructure under weather extremes. In this paper, the time-varying model for resilience recovery of civil airport infrastructure under weather extremes is proposed based on the Cox proportional hazard model. The flight weather extremes events of the USA civil aviation flight data of 2019 are selected to establish the database for the analysis of resilience recovery of civil airport infrastructure, which includes 10 covariates. The statistical significance and risk rate of the covariates are investigated by the single factor method and PH assumption. The influence of covariates on the resilience level and recovery time of the civil airport infrastructure is explored. The results indicate that the rainfall, snow depth, delayed flight volume, low temperature, and crosswind are significant factors for the resilience recovery of civil airport infrastructure, and the regression coefficients of low temperature and crosswind are larger than the others. The key period for functional recovery of civil airport infrastructure is within 900 min after the weather extremes occurs. When the resilience function reaches to 50%, the recovery time of the infrastructure system increases by 30.0% and 26.2% considering the low temperature and crosswind respectively.