In this paper, we propose a new stochastic variance reduction gradient algorithm for minimizing the sum of a finite number of smooth convex functions in machine learning. The characteristic of the new algorithm is to combine the gradient algorithm of stochastic variance reduction and a method of spectral gradient BB step size, so that the advantages of the two methods can be fully utilized. In addition, the new algorithm uses the important sample sampling method, which can greatly reduce the computation workload. In the end, it is proved that the new algorithm has R-linear convergence rate under the usual assumptions, and the complexity analysis is given. Numerical experiments show that the new algorithm is feasible and effective.