Recent advancements in Large Language Models (LLMs) have shown remarkable performance across a wide range of tasks. Despite this, the auto-regressive nature of LLM decoding, which generates only a single token per forward propagation, fails to fully exploit the parallel computational power of GPUs, leading to considerable latency. To address this, we introduce a novel speculative decoding method named FIRP which generates multiple tokens instead of one at each decoding step. We achieve this by predicting the intermediate hidden states of future tokens (tokens have not been decoded yet) and then using these pseudo hidden states to decode future tokens, specifically, these pseudo hidden states are predicted with simple linear transformation in intermediate layers of LLMs. Once predicted, they participate in the computation of all the following layers, thereby assimilating richer semantic information. As the layers go deeper, the semantic gap between pseudo and real hidden states is narrowed and it becomes feasible to decode future tokens with high accuracy. To validate the effectiveness of FIRP, we conduct extensive experiments, showing a speedup ratio of 1.9x-3x in several models and datasets, analytical experiments also prove our motivations.