FlashAttention series has been widely applied in the inference of large language models (LLMs). However, FlashAttention series only supports the high-level GPU architectures, e.g., Ampere and Hopper. At present, FlashAttention series is not easily transferrable to NPUs and low-resource GPUs. Moreover, FlashAttention series is inefficient for multi- NPUs or GPUs inference scenarios. In this work, we propose FastAttention which pioneers the adaptation of FlashAttention series for NPUs and low-resource GPUs to boost LLM inference efficiency. Specifically, we take Ascend NPUs and Volta-based GPUs as representatives for designing our FastAttention. We migrate FlashAttention series to Ascend NPUs by proposing a novel two-level tiling strategy for runtime speedup, tiling-mask strategy for memory saving and the tiling-AllReduce strategy for reducing communication overhead, respectively. Besides, we adapt FlashAttention for Volta-based GPUs by redesigning the operands layout in shared memory and introducing a simple yet effective CPU-GPU cooperative strategy for efficient memory utilization. On Ascend NPUs, our FastAttention can achieve a 10.7$\times$ speedup compared to the standard attention implementation. Llama-7B within FastAttention reaches up to 5.16$\times$ higher throughput than within the standard attention. On Volta architecture GPUs, FastAttention yields 1.43$\times$ speedup compared to its equivalents in \texttt{xformers}. Pangu-38B within FastAttention brings 1.46$\times$ end-to-end speedup using FasterTransformer. Coupled with the propose CPU-GPU cooperative strategy, FastAttention supports a maximal input length of 256K on 8 V100 GPUs. All the codes will be made available soon.