Vision-based ego-velocity estimation is a fundamental problem in robot state estimation. However, the constraints of frame-based cameras, including motion blur and insufficient frame rates in dynamic settings, readily lead to the failure of conventional velocity estimation techniques. Mammals exhibit a remarkable ability to accurately estimate their ego-velocity during aggressive movement. Hence, integrating this capability into robots shows great promise for addressing these challenges. In this paper, we propose a brain-inspired framework for linear-angular velocity estimation, dubbed NeuroVE. The NeuroVE framework employs an event camera to capture the motion information and implements spiking neural networks (SNNs) to simulate the brain's spatial cells' function for velocity estimation. We formulate the velocity estimation as a time-series forecasting problem. To this end, we design an Astrocyte Leaky Integrate-and-Fire (ALIF) neuron model to encode continuous values. Additionally, we have developed an Astrocyte Spiking Long Short-term Memory (ASLSTM) structure, which significantly improves the time-series forecasting capabilities, enabling an accurate estimate of ego-velocity. Results from both simulation and real-world experiments indicate that NeuroVE has achieved an approximate 60% increase in accuracy compared to other SNN-based approaches.