In this paper, we present a user model of subjective quality assessment on virtual viewpoint image (VVI) for free-viewpoint video system. VVIs are rendered through neighbor viewpoint color and depth images, and it is a new type of image that generated for human-computer interaction (HCI) in free-viewpoint video system. In this system, a natural scene is captured by multi-viewpoint cameras, and users can view the scene from any desired viewpoint, regardless the real or virtual one. The subjective quality of VVIs is crucial for the quality of experiences for HCI, because the magnitude of VVI is much greater than the real. In order to find the user model of VVI quality assessment, we organize three sets of stimuli, including Symmetric Stimuli, Asymmetric Stimuli Part I and Part II, to reveal the psychological responses of participants. A psychometric function is consequently obtained to determine the relationship between stimulus and psychological responses. Further discussions on the factors of distortion level, gender, age and academic background are examined to find the influence on the user model. We find that the distortion level of neighbor viewpoint color images has the dominant impact on the user model, while other factors contribute little.