A sparse coefficients wavelength selection and regression (SCWR) method is proposed in the present study. SCWR can rapidly and simultaneously operate regression and select wavelengths on NIR datasets with multiple response variables without any random procedure and cross-validation in the model. The method expresses a normal spectral calibration as a form of least absolute shrinkage and selection operator (LASSO), then the problem is reformulated into the alternative direction multiplier method (ADMM) form. Sparse coefficients wavelength selection (SCWS) method is developed by planting a positive-negative counteract strategy into SCWR, it can select a specified number of wavelengths. A specified number SCWR (NSCWR) is also suggested in order to perform regression using a specified number of wavelengths. SCWR methods have been tested on three NIR datasets (potato, corn, and soil), and these methods have better performance and use fewer feature wavelengths than existing simultaneous regression and wavelength selection methods on predicting almost all attributes in these datasets. Results indicate that SCWR-based methods could select wavelengths with more useful information. For the determination of hyperparameters in SCWR, manual adjustment of hyperparameters is available on sparsity control because the regression performance of SCWR is robustness and insensitive when hyperparameters are in proper ranges.