Accurate and timely monitoring of biochemical and biophysical traits associated with crop growth is essential for indicating crop growth status and yield prediction for precise field management. This study evaluated the application of three combinations of feature selection and machine learning regression techniques based on unmanned aerial vehicle (UAV) multispectral images for estimating the bio-parameters, including leaf area index (LAI), leaf chlorophyll content (LCC), and canopy chlorophyll content (CCC), at key growth stages of winter wheat. The performance of Support Vector Regression (SVR) in combination with Sequential Forward Selection (SFS) for the bio-parameters estimation was compared with that of Least Absolute Shrinkage and Selection Operator (LASSO) regression and Random Forest (RF) regression with internal feature selectors. A consumer-grade multispectral UAV was used to conduct four flight campaigns over a split-plot experimental field with various nitrogen fertilizer treatments during a growing season of winter wheat. Eighteen spectral variables were used as the input candidates for analyses against the three bio-parameters at four growth stages. Compared to LASSO and RF internal feature selectors, the SFS algorithm selects the least input variables for each crop bio-parameter model, which can reduce data redundancy while improving model efficiency. The results of the SFS-SVR method show better accuracy and robustness in predicting winter wheat bio-parameter traits during the four growth stages. The regression model developed based on SFS-SVR for LAI, LCC, and CCC, had the best predictive accuracy in terms of coefficients of determination (R2), root mean square error (RMSE) and relative predictive deviation (RPD) of 0.967, 0.225 and 4.905 at the early filling stage, 0.912, 2.711 μg/cm2 and 2.872 at the heading stage, and 0.968, 0.147 g/m2 and 5.279 at the booting stage, respectively. Furthermore, the spatial distributions in the retrieved winter wheat bio-parameter maps accurately depicted the application of the fertilization treatments across the experimental field, and further statistical analysis revealed the variations in the bio-parameters and yield under different nitrogen fertilization treatments. This study provides a reference for monitoring and estimating winter wheat bio-parameters based on UAV multispectral imagery during specific crop phenology periods.