The stochastic recursive gradient algorithm (SARAH)  attracts much interest recently. It admits a simple recursive framework for updating stochastic gradient estimates. Motivated by this, in this paper, we propose a SARAH-I method incorporating importance sampling, whose linear conver- gence rate of the sequence of distances between iterates and the optima set is proven under both strong convexity and non-strong convexity conditions. Fur- ther, we propose to use the Barzilai-Borwein (BB) method to automatically compute step sizes for SARAH-I, named as SARAH-I-BB, and we establish its convergence and complexity properties in different cases. Finally numerical tests are reported to indicate promising performances of SARAH-I-BB.