Convex composition optimization is an emerging topic that covers a wide range of applications arising from stochastic optimal control, reinforcement learning and multi-stage stochastic programming. Existing algorithms suffer from unsatisfactory sample complexity and practical issues since they ignore the convexity structure in the algorithmic design. In this paper, we develop a new stochastic compositional variance-reduced gradient algorithm with the sample complexity of O((m+n)log(1/ϵ)+1/ϵ^3) where m+n is the total number of samples. Our algorithm is near-optimal as the dependence on m+n is optimal up to a logarithmic factor. Experimental results on real-world datasets demonstrate the effectiveness and efficiency of the new algorithm.