Soil potassium content affects the quality and yield of crops. In this study, near-infrared (NIR) spectroscopy is combined with a method of selecting feature wavebands for the rapid quantitative detection of soil potassium content. First, the NIR model for the feature waveband optimization of the soil potassium content is established by combining the simulated annealing algorithm and interval partial least squares (SA-iPLS). Then, the optimal feature waveband of SA-iPLS is obtained by adjusting the number of subintervals. Finally, the SA-iPLS model is compared with the partial least squares (PLS), interval PLS (iPLS), and synergy iPLS (SiPLS) models according to the evaluation indicators of the model. The results show that the SA-iPLS model exhibited the best performance on the training set when the number of subintervals is 90, and the prediction root mean square error and correlation coefficient of the test set are 0.0117 and 0.8884, respectively. The prediction root mean square error and correlation coefficient of the full-spectrum PLS model for the test set samples are 0.0140 and 0.8506, respectively. The optimal number of subintervals for the iPLS and SiPLS models are 80 and 70, respectively; the prediction root mean square errors for the test set samples are 0.0155 and 0.0145, respectively; the correlation coefficients are 0.7786 and 0.8420, respectively. Compared to the conventional iPLS and SiPLS models, the SA-iPLS model can retain more useful spectral information and improve the prediction accuracy of the soil potassium content.