During load-following operation of nuclear power plants, thermal-hydraulic parameters exhibit dynamic coupling, time delays, and nonlinear dependencies. Conventional synchronous correlation analysis is often insufficient to fully characterize such dynamic relationships. To address this issue, this study proposes a DTLCC-MI (Differenced Time-Lagged Cross-Correlation and Mutual Information) method by combining differenced time-lagged cross-correlation with mutual information for parameter correlation analysis and key feature selection during load-following transients. The method first applies differencing to extract the dynamic variations of the parameters. Time-lagged cross-correlation is then used to identify the optimal time lag and corresponding correlation strength between candidate parameters and target variables. After temporal alignment based on the identified lag, mutual information is calculated to characterize nonlinear dependencies between variables, while the stability of parameter relationships under different load-following conditions is also evaluated. Based on PCTran-generated load-following transient data, 31 candidate thermal-hydraulic parameters and four key target variables, including reactor power, average coolant temperature, pressurizer pressure, and pressurizer water level, were selected, resulting in 124 parameter-target combinations for analysis. The results show that DTLCC-MI can identify the dynamic dependencies and time-lag characteristics between different parameters and target variables, and can further select key parameters with strong correlations and high stability across different operating conditions. The proposed method provides a basis for feature selection and parameter modeling in state prediction of nuclear power plants under load-following conditions.