Recently, deep learning-based models such as transformer have achieved significant performance for industrial remaining useful life (RUL) prediction due to their strong representation ability. In many industrial practices, RUL prediction algorithms are deployed on edge devices for real-time response. However, the high computational cost of deep learning models makes it difficult to meet the requirements of edge intelligence. In this article, a lightweight group transformer with multihierarchy time-series reduction (GT-MRNet) is proposed to alleviate this problem. Different from most existing RUL methods computing all time series, GT-MRNet can adaptively select necessary time steps to compute the RUL. First, a lightweight group transformer is constructed to extract features by employing group linear transformation with significantly fewer parameters. Then, a time-series reduction strategy is proposed to adaptively filter out unimportant time steps at each layer. Finally, a multihierarchy learning mechanism is developed to further stabilize the performance of time-series reduction. Extensive experimental results on the real-world condition datasets demonstrate that the proposed method can significantly reduce up to 74.7% parameters and 91.8% computation cost without sacrificing accuracy.