Fast, accurate, and non-destructive detection of the nitrogen (N) content in corn leaves is of great significance for the precise dynamic management of nitrogen fertilizer application for corn. Hyperspectral data can provide an important means for detecting the nitrogen content in plants. Existing research has mainly focused on using various vegetation indices or 3–5 band combinations to estimate leaf nitrogen content, ignoring the different in spectral characteristics of hyperspectral data and failing to characterize most of the spectral information. Some scholars have used principal component analysis and wavelet analysis dimensionality reduction algorithms, but used different bands for these models. Therefore, more and different inversion models need to be introduced to improve the use of spectral data and increase the universality of the model. The present study selected three different methods to reduce data dimensionality, including the Successful Projections Algorithm (SPA) and the Least Absolute Shrinkage and Selection Operator (LASSO) and the Elastic Net (EN) algorithms. Then the processed spectral reflectance information and observational data for synchronous leaf nitrogen content were used to construct an inversion model used to predict leaf nitrogen content. Nine inversion models were constructed based on different dimensionality reduction and regression methods. Based on the coefficient of determination (R2) and root mean square error (RMSE), the accuracy of each model was tested. The main results follow: (1) Dimensionality reduction processing of hyperspectral data can effectively prevent data from overfitting, limit the correlation between adjacent frequency bands, and reduce data redundancy. An EN dimensionality reduction algorithm (EN-Partial Least Squares Regression (PLSR)) model R2 = 0.96, RMSE = 0.19) was better than a SPA (SPA-PLSR model R2 = 0.90, RMSE = 0.26) and LASSO (LASSO-PLSR model R2 = 0.89, RMSE = 0.37) dimensionality reduction algorithm. (2) For the same dimensionality reduction method, the accuracy of the regression model based on PLSR was higher than that of other models. Among the nine inversion models in this paper, the EN-PLSR inversion model has the best fitting effect (R2 = 0.96, RMSE = 0.19). (3) Obvious changes in nitrogen content have little effect on the overall hyperspectral reflectance curve. This study provides a reference for high-efficiency and non-destructive testing of corn nitrogen content using hyperspectral technology.