Achieving high image quality for temporal frames in dynamic positron emission tomography (PET) is challenging due to the limited statistic especially for the short frames. Recent studies have shown that deep learning (DL) is useful in a wide range of medical image denoising tasks. In this paper, we propose a model-based neural network for dynamic PET image denoising. The inter-frame spatial correlation and intra-frame structural consistency in dynamic PET are used to establish the kernel space-based multidimensional sparse (KMDS) model. We then substitute the inherent forms of the parameter estimation with neural networks to enable adaptive parameters optimization, forming the end-to-end neural KMDS-Net. Extensive experimental results from simulated and real data demonstrate that the neural KMDS-Net exhibits strong denoising performance for dynamic PET, outperforming previous baseline methods. The proposed method may be used to effectively achieve high temporal and spatial resolution for dynamic PET. Our source code is available at https://github.com/Kuangxd/Neural-KMDS-Net/tree/main.