Wheat variety identification is an essential component of the official inspection of wheat grains to determine their quality and trade value. Traditionally, wheat class identification requires deep knowledge about the appearance of plants and kernels, their history and distribution. Therefore, there is an urgent need for an automatic technology to standardize the nomenclature of wheat varieties to enable both growers and producers to identify their grains practically. The present study investigated the feasibility of Visible-Near Infrared (Vis-NIR) and Short-Wave Infrared (SWIR) spectral imaging to identify wheat classes. Both sides of the wheat kernel as single kernel measurements and bulk grains were used to acquire hyperspectral data and vertical and horizontal data concatenation was implemented to explore performance differences. In addition, the classification of bulk kernels from single kernel data was investigated. Spectral data was pre-treated by standard normal variate (SNV), Savitzky-Golay first (SG-1) and second derivatives (SG-2) and linear discriminant analysis (LDA), support vector machine (SVM) and artificial neural network (ANN) were applied as the classification algorithms. Furthermore, feature selection was utilised using the minimum redundancy maximum relevance (mRMR) algorithm to investigate the performance difference between data concatenation and feature selection. The results showed that ventral (up) side data showed better classification performances than reverse (down) side data, while Vis-NIR data achieved higher classification accuracies than SWIR data. However, the best classification performance for single kernels was obtained by LDA-SNV using up and down data in the Vis-NIR and SWIR regions vertically and horizontally concatenated with an accuracy of 93.72% for 10-fold cross-validation and 94.93% for test sets. Models based on a hundred features did not achieve the accuracy of models based on concatenated data. Moreover, classification performances of bulk samples were higher than single kernels, which achieved 100% accuracy for both cross-validation and test sets. The study demonstrates that spectral imaging has a high potential to identify wheat classes non-destructively.