In this paper, we present a segmentation and classification method for thyroid follicular neoplasms based on a combination of the prior-based level set method and deep convolutional neural network. The proposed method aims to discriminate thyroid follicular adenoma (TFA) and follicular thyroid carcinoma (FTC) in ultrasound images. In their appearance, these two kinds of tumours have similar shapes, sizes and contrasts. Therefore, it is difficult for even ultrasound specialists to distinguish them. Because of the complex background in thyroid ultrasound images, before distinguishing TFA and FTC, we need to segment the lesions from the whole image for each patient. The main challenge of segmentation is that the images often have weak edges and heterogeneous regions. The main issue of classification is that the accuracy depends on the features extracted from the segmentation results. To solve these problems, we conduct the two tasks, i.e. segmentation and classification, by a cascaded learning architecture. For segmentation, to obtain more accurate results, we exploit the Res-U-net framework and the prior-based level set method to enhance their respective abilities. Then, the classification network is trained by sharing shallow layers of the segmentation network. Testing the proposed method on real patient data shows that it is able to segment the lesion areas in thyroid ultrasound images with a Dice score of 92.65% and to distinguish TFA and FTC with a classification accuracy of 96.00%.