Emotion distribution learning (EDL) handles emotion fuzziness by means of the emotion distribution, which is an emotion vector that quantitatively represents a set of emotion categories with their intensity of a given instance. Despite successful applications of EDL in many practical emotion analysis tasks, existing EDL methods have seldom considered the linguistic prior knowledge of affective words specific to the text mining task. To address the problem, this paper proposes a text emotion distribution learning model based on a lexicon-enhanced multi-task convolutional neural network (LMT-CNN) to jointly solve the tasks of text emotion distribution prediction and emotion label classification. The LMT-CNN model designs an end-to-end multi-module deep neural network to utilize both semantic information and linguistic knowledge. Specifically, the architecture of the LMT-CNN model consists of a semantic information module, an emotion knowledge module based on affective words, and a multi-task prediction module to predict emotion distributions and labels. Extensive comparative experiments on nine commonly used emotional text datasets showed that the proposed LMT-CNN model is superior to the compared EDL methods for both emotion distribution prediction and emotion recognition tasks.