Human beings not only have the ability of logical reasoning, but also can produce, control and express emotions. Making computers have the ability of generating emotions is a challenging task of affective computing. In this paper, we construct an emotion generation model using cognitive maps and show the generated emotions with 3D facial expression animation. This paper first introduces some basic theories about emotion, reviews some typical emotion models and compares their strengths and weaknesses. According to the characteristics of emotion, we use the PAD (Pleasure-Arousal-Dominance) emotion space to describe the emotion and mood. In the same time, we adopt the Five Factor Model to define the personality trait and discuss the relationships between the three main affective elements.Secondly, we introduce the theories of cognitive map and construct the emotion generation model using cognitive maps. The model is used to generate emotion based on the evaluation of the overall influences of the mood, the personality, the previous emotion, and the external stimulations. A cognitive map is a graph model for the expressing and reasoning the causal relationships between cause and effect concepts. It can be seen as a network with symbols and feedbacks. So the generation model works effectively and meets the basic principle of human emotion generation.To demonstrate the emotion generation model intuitively, we use a vivid 3D facial expression to show the results of the emotion generation. A mapping mechanism between the emotion space and the facial expression space is built. We construct the facial expressions according to the 24 basic emotions with a realistic 3D head, and complete the real 3D facial expression animation by interpolation.At last, we design an intelligent virtual human system with vivid facial expressions, visual speech and some vision. The virtual head can have emotional communication with the users. The experimental results show that the emotion generation model using cognitive map can produce realistic emotions similar to those of a real human.