Early disease identification in crops is critical for food security, especially in Sub-Saharan Africa. To identify cassava diseases, professionals visually score the plants by looking for disease indicators on the leaves which is notoriously subjective. Automating the detection and classification of crop diseases could help professionals diagnose diseases more accurately and allow farmers in remote locations to monitor their crops without the help of specialists. Machine learning algorithms have been used in the early detection and classification of crop diseases. However, traditional machine learning algorithms are not calibrated even though they have high accuracy. The ability to provide well-calibrated posterior distributions is one of the most appealing properties of Gaussian processes. Motivated by the current developments in the field of Gaussian Processes, this study proposed a deep Gaussian convolutional neural network model (DGCNN) for the detection and classification of cassava diseases using spectral data. The proposed model uses a hybrid kernel function that is the product of a rational quadratic kernel and a squared exponential kernel. Experimental results revealed that our proposed hybrid kernel function performed better in terms of accuracy of 90.10% when compared to both the squared exponential kernel with an accuracy of 88.01% and the rational quadratic kernel with an accuracy of 88.52%. In our future work, we propose to integrate the Optimised model proposed in this study with the transfer learning approach, a move that may help to improve the model performance.