Accurate classification of laryngeal cancer is a critical step for diagnosis and appropriate treatment. Radiomics is a rapidly advancing field in medical image processing that uses various algorithms to extract many quantitative features from radiological images. The high dimensional features extracted tend to cause overfitting and increase the complexity of the classification model. Thereby, feature selection plays an integral part in selecting relevant features for the classification problem. In this study, we explore the predictive capabilities of radiomics on Computed Tomography (CT) images with the incidence of laryngeal cancer to predict the histopathological grade and T stage of the tumour. Working with a pilot dataset of 20 images, an experienced radiologist carefully annotated the supraglottic lesions in the three-dimensional plane. Over 280 radiomic features that quantify the shape, intensity and texture were extracted from each image. Machine learning classifiers were built and tested to predict the stage and grade of the malignant tumour based on the calculated radiomic features. To investigate if radiomic features extracted from CT images can be used for the classification of laryngeal tumours. Out of 280 features extracted from every image in the dataset, it was found that 24 features are potential classifiers of laryngeal tumour stage and 12 radiomic features are good classifiers of histopathological grade of the laryngeal tumor. The novelty of this paper lies in the ability to create these classifiers before the surgical biopsy procedure, giving the clinician valuable, timely information.