(1) Background: To achieve the rapid, non-destructive detection of corn freshness and staleness for better use in the storage, processing and utilization of corn. (2) Methods: In this study, three varieties of corn were subjected to accelerated aging treatment to study the trend in fatty acid values of corn. The study focused on the use of hyperspectral imaging technology to collect information from corn samples with different aging levels. Spectral data were preprocessed by a convolutional smoothing derivative method (SG, SG1, SG2), derivative method (D1, D2), multiple scattering correction (MSC), and standard normal transform (SNV); the characteristic wavelengths were extracted by the competitive adaptive reweighting method (CARS) and successive projection algorithm (SPA); a neural network (BP) and random forest (RF) were utilized to establish a prediction model for the quantification of fatty acid values of corn. And, the distribution of fatty acid values was visualized based on fatty acid values under the corresponding optimal prediction model. (3) Results: With the prolongation of the aging time, all three varieties of corn showed an overall increasing trend. The fatty acid value of corn can be used as the most important index for characterizing the degree of aging of corn. SG2-SPA-RF was the quantitative prediction model for optimal fatty acid values of corn. The model extracted 31 wavelengths, only 12.11% of the total number of wavelengths, where the coefficient of determination RP2 of the test set was 0.9655 and the root mean square error (RMSE) was 3.6255. (4) Conclusions: This study can provide a reliable and effective new method for the rapid non-destructive testing of corn freshness.