Sub-band models have achieved promising results due to their ability to model local patterns in the spectrogram. Some studies further improve the performance by fusing sub-band and full-band information. However, the structure for the full-band and sub-band fusion model was not fully explored. This paper proposes a dual-path transformer-based full-band and sub-band fusion network (DPT-FSNet) for speech enhancement in the frequency domain. The intra and inter parts of the dual-path transformer model sub-band and full-band information, respectively. The features utilized by our proposed method are more interpretable than those utilized by the time-domain dual-path transformer. We conducted experiments on the Voice Bank + DEMAND and Interspeech 2020 Deep Noise Suppression (DNS) datasets to evaluate the proposed method. Experimental results show that the proposed method outperforms the current state-of-the-art.