In many virtual reality applications the virtual human, as the digital representation of human, is one of the most important elements to improve the interactive capability and immersive experience. However, it remains a challenge for modeling virtual human to synthesize natural and controllable motions. This paper presents a novel method for motion synthesis based on functional data analysis. A low-dimensional functional space is constructed from a set of example motions by using functional principal components analysis. This functional space can not only discover the true dimension of the examples, but also provide an approach to synthesize natural and smooth motions with purpose by controlling the coefficients of each functional basis. This synthesis process is very efficient because there is no time-consuming calculation, which can meet the requirement of real-time applications. The experiments have proven the robustness and effectiveness of this method.