Different parts of ayurvedic herbal plants are used to make ayurvedic medicines in Sri Lanka. Recognising these endemic herbal plants is a challenging problem in the fields of ayurvedic medicine, computer vision, and machine learning. In this research, a computer system has been developed to recognise ayurvedic plant leaves in Sri Lanka based on a recently developed machine learning algorithm: convolutional neural networks (CNNs). Convolutional neural networks with RGB and grayscale images and multi-layer neural networks with RGB images have been used to recognise the ayurvedic plant leaves. In order to train neural networks, images of 17 types of herbal plant leaves were captured from the plant nursery of Navinna Ayurveda Medical Hospital, Sri Lanka. As CNNs require a large number of images to train it, various data augmenting methods have been applied to the collected dataset to increase the size of the dataset. Backgrounds of images were removed and all images were resized to 256 by 256 pixels before submitting them to a neural network. The results obtained were highly significant and CNN with RGB images was able to achieve an accuracy of 97.71% for recognising ayurvedic herbal plant leaves in Sri Lanka. The study suggests that CNNs can be used to recognise ayurvedic herbal plants.