Recently, significant progress has been made in seizure prediction, attributed to the advancement of basic models. Specifically, the structures combining convolutional networks with transformers can successfully extract both local and global features. However, the disadvantage of the transformer is also inherited, namely, the quadratic computational complexity with respect to the length of the sequence. Inspired by the recent model with linear complexity for long-distance modeling, named Mamba, we explore the potential of this state space model for the seizure prediction task in terms of effectiveness and efficiency in the paper. Nevertheless, directly applying Mamba yields poor performance since multi-scale global and local features are not taken into consideration. To address this issue, we propose a novel design called MambaFuse. Specifically, a parallel Mamba and CNN block is initially developed to extract multi-scale global and local features. Firstly, the multi-scale Mamba module is proposed to leverage the global modeling of Mamba at linear complexity. Secondly, the scale-adapt CNN module is proposed to extract local features through residual learning. Finally, the enhanced cross-attention fusion module is proposed to dynamically combine global Mamba features and local convolution features for a multi-scale global-local representation. Experimental results on the dataset of CHB-MIT have demonstrated that MambaFuse outperforms state-of-the-art methods, providing a promising approach for seizure prediction.