Elastic registration is regarded as a key task in medical image processing， whose performance directly affects the accuracy of subsequent tasks such as segmentation， classification， and prediction. However， due to the insensitivity of neural networks to high-frequency components， the existing methods have difficulty in capturing high-frequency information in images， which affects the fitting accuracy of registration field. To address this issue， a high-frequency-preserving medical image registration model based on frequency spectrum decomposition — DFRes （Decomposition in Frequency domain model for Registration） was proposed. In the model， a frequency decomposition strategy was introduced， and a dual-branch structure was adopted to process high- and low-frequency information from the original image. Meanwhile， an Invertible Neural Network （INN） structure with high-frequency preservation characteristics and a bridge-style feature fusion module with ability to fuse high- and low-frequency information were designed， and an alternating spatial-frequency information extraction module was used to further enhance the model’s ability to extract and fuse frequency- and spatial-domain information. Experimental results of comparing DFRes and the existing advanced models on the IXI， OSSAI， and Huaxi rectal cancer datasets show that DFRes achieves significant improvements on multiple metrics. On IXI dataset， compared to the TransMorph model， DFRes has the Dice Similarity Coefficient （DSC） increased by 2.5 percentage points， the Average Surface Distance （ASD） reduced by 0.012， and the Structural SIMilarity （SSIM） increased by 1.6 percentage points. At the same time， the effectiveness of the module design is verified through ablation experiments.