The cerebellum plays an important role in smooth and coordinated motor control. Precise control requires the cerebellum to regulate movements in both space and time domains. Although many cerebellar models have been proposed, most of them focus on motor coordination, motor learning, or timing distinctly. Therefore, it is necessary to develop a cerebellar model which contributes to the proper execution of movements via motor learning that displays temporal specificity. In this paper, we proposed a novel spiking neural network model to realize cerebellar processing with strong biomimicry, which is based on adapting rate neurons and has a cerebellum-inspired structure as well as biologically plausible cerebellar divergence/convergence ratios. The model was tested with the eyeblink classical conditioning (EBCC) experimental task. The simulation results verify that our implementation has improvements in both signal encoding and learning speed than previous studies. Furthermore, compared with neurophysiological data, our model shows a similar learning trend and can represent the fluctuation of the learning curves. It is demonstrated that our proposed cerebellar model experimentally reproduces the key features of the EBCC task and provides a new way to understand the timing and learning control neural mechanisms of the cerebellum.