Spiking neural network (SNN) has attracted great attention due to its characteristic of high efficiency and accuracy. Currently, the ANN-to-SNN conversion methods can obtain ANN on-par accuracy SNN with ultra-low latency (8 time-steps) in CNN structure on computer vision (CV) tasks. However, as Transformer-based networks have achieved prevailing precision on both CV and natural language processing (NLP), the Transformer-based SNNs are still encounting the lower accuracy w.r.t the ANN counterparts.In this work, we introduce a novel ANN-to-SNN conversion method called SpikeZIP-TF, where ANN and SNN are exactly equivalent, thus incurring no accuracy degradation. SpikeZIP-TF achieves 83.82\% accuracy on CV dataset (ImageNet) and 93.79\% accuracy on NLP dataset (SST-2), which are higher than SOTA Transformer-based SNNs.