There are differences in spectral data acquisition equipment and environmental conditions. In near-infrared spectroscopy quantitative analysis, low prediction accuracy was found in the models established. To enhance the universality and generalizability of near-infrared spectroscopy quantitative analysis models and improve their predictive accuracy, a universal model strategy is proposed based on the transfer component analysis method improved by the transfer matrix (TM-TCA). The TM-TCA method adopts a two-step correction strategy to correct the slave spectral data, reducing the spectral differences caused by instrument offsets, drifts, or instabilities. It can make the characteristics of the corrected slave spectral data similar to the master’s to the maximum extent, eliminate the deviation caused by different instruments or external conditions, and enhance the prediction ability of the model to the slave spectral data. Firstly, the spectral transfer matrix between the master and the slave is obtained. The transfer matrix converts the master-slave spectral data matrix, which is then used as the input for the transfer component analysis method. Subsequently, the kernel function and the number of eigenvalues in transfer learning are chosen using iterative optimization of multiple indicators. The RBF kernel function is selected, and the number of eigenvalues is 52. Comparative experiments are conducted with other methods to verify the effectiveness of TM-TCA. The experimental results show that the spectral correction rate based on TM-TCA reaches 97.1%, with a reduction of 82.9% in the average relative mean squared (ARMS). The ARMS value surpasses that achieved by the transfer matrix and TCA methods, 46.5% and 30.2%, respectively. To validate the effectiveness of the model construction strategy, a universality quantitative analysis model is established based on TM-TCA and partial least squares regression (PLSR) under different device conditions. Compared to the prediction performance, the TCA-PLSR model’s coefficient of determination of the TM-TCA-PLSR model reaches 0.872 9, which is improved by 41%. The root-mean-square error of prediction (RMSEP) and the mean absolute error (MAE) are 0.154 3 and 0.115 9, respectively, reduced by more than 90%. Furthermore, the relative prediction determination (RPD) of the TM-TCA-PLSR model exceeds 2.5, indicating that the model has practical application value. The experimental results demonstrate that the TM-TCA transfer method reduces the difference between the master and slave spectra. The master model established based on TM-TCA exhibits a certain degree of universality capability.