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Multi-goal reinforcement learning is widely applied in planning and robot manipulation. Two main challenges in multi-goal reinforcement learning are sparse rewards and sample inefficiency. Hindsight Experience Replay (HER) aims to tackle the two challenges via goal relabeling. However, HER-related works still need millions of samples and a huge computation. In this paper, we propose Multi-step Hindsight Experience Replay (MHER), incorporating multi-step relabeled returns based on -step relabeling to improve sample efficiency. Despite the advantages of -step relabeling, we theoretically and experimentally prove the off-policy -step bias introduced by -step relabeling may lead to poor performance in many environments. To address the above issue, two bias-reduced MHER algorithms, MHER() and Model-based MHER (MMHER) are presented. MHER() exploits the return while MMHER benefits from model-based value expansions. Experimental results on numerous multi-goal robotic tasks show that our solutions can successfully alleviate off-policy -step bias and achieve significantly higher sample efficiency than HER and Curriculum-guided HER with little additional computation beyond HER.