Rapid and non-destructive estimation of the chlorophyll content in cotton leaves is of great significance for the real-time monitoring of cotton growth under verticillium wilt (VW) stress. The spectral reflectance of healthy and VW cotton leaves was determined using hyperspectral technology, and the original spectra were processed using Savitzky–Golay (SG) smoothing, and on its basis through mean centering, standard normal variate (SG-SNV), multiplicative scatter correction (SG-MSC), reciprocal second-order differentiation, and logarithmic second-order differentiation ([lg(SG)]″) preprocessing operations. The characteristic bands were selected based on the correlation coefficient, vegetation index, successive projection algorithm (SPA), and competitive adaptive reweighted sampling (CARS). The single-factor model, back propagation neural network of particle swarm optimization algorithm, and extreme learning machine (ELM) of a grey wolf optimizer (GWO) algorithm were constructed to compare and explore the ability of each model to estimate the soil plant analysis development (SPAD) value of cotton under VW stress. The results showed that spectral pretreatment could improve the correlation between characteristic bands and SPAD values. SG-MSC and SG-SNV showed better changes in the five pretreatments, and the maximum correlation coefficients of healthy and VW cotton leaves were higher than 0.74. Compared with SPA, the accuracy of model estimation based on CARS-extracted characteristic bands was higher, and the estimation accuracy of the multi-factor model was better than that of the single-factor model under each pretreatment. For healthy cotton leaves, [lg(SG)]″–CARS–GWO–ELM was the optimal model, with a modeling and validation set R2 of 0.956 and 0.887, respectively. For VW cotton leaves, SG-MSC–CARS–GWO–ELM was the optimal model, with a modeling and validation set R2 of 0.832 and 0.824, respectively. Therefore, the GWO–ELM model constructed under different pretreatments combined with characteristic extraction methods can be used for the estimation of leaf SPAD values under VW stress to dynamically monitor VW stress in cotton and provide a theoretical reference for precision agriculture.