Deep learning is revolutionizing the already rapidly developing field of computer vision. The convolutional neural network (CNN) is a state-of-the-art deep learning tool that learns high level features directly from a huge dataset of labeled images. In document image processing, ink analysis allows for determination of ink age and forgery and identification of pen or writer. The spectral information of inks in hyperspectral document images provides valuable information about the underlying material and thus helps in identification and discrimination of inks based on their unique spectral signatures even if they have the same color. Ink mismatch detection is a key step in document forgery detection. Although various ink mismatch detection techniques are available in the recent literature, there is a constant need for development of more accurate and effective methods to empower automated document forgery detection. A state-of-the-art deep learning method for ink mismatch detection in hyperspectral document images is proposed. The spectral responses of ink pixels are extracted from a hyperspectral document image, reshaped to a CNN-friendly image format and fed to the CNN for classification. The proposed method effectively identifies different ink types in a hyperspectral document image for forgery detection and achieves an overall accuracy of 98.2% for blue and 88% for black inks, which is the highest accuracy among the latest techniques of ink mismatch detection on the UWA Writing Ink Hyperspectral Images (WIHSI) database and differentiates between the highest number of inks mixed in unbalanced proportions in a hyperspectral document image. Furthermore, a detailed discussion on selection of appropriate CNN architecture and classification results are presented in this paper along with comparison with the former methods of ink mismatch detection. This research opens a new window for research on automated forgery detection in hyperspectral document images using deep learning.