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The anisotropic elastic wave equations can be used to stimulate the attributes of wave traveling through the earth more precisely than acoustic approximations. However, the first-order derivatives calculated by conventional finite-difference method leads to lots of artifacts on the modeling results, which would damage the imaging results of reverse time migration. We have employed rotated staggered-grid finite-difference techniques on second-order system and obtained obvious improvements of the modeling results. Most importantly, we make comparisons of our new scheme and classical staggered-grid scheme in accuracy, memory requirements and acceleration performance aspects, respectively. Numerical experiments demonstrate that our new scheme has comparable accuracy and speedup with classical one. Hence, we provide a feasible and alternative scheme for anisotropic elastic wave modeling, which is essential to reverse time migration imaging.