Event cameras are bio-inspired sensors that asynchronously capture per-pixel brightness change and trigger a stream of events instead of frame-based images. Each event stream is generally split into multiple sliding windows for subsequent processing. However, most existing event-based methods ignore the motion continuity between adjacent spatiotemporal windows, which will result in the loss of dynamic information and additional computational costs. To efficiently extract strong features for event streams containing dynamic information, this paper proposes a novel memory-based network with dual-branch, namely MENet. It contains a base branch with a full-sized event point-wise processing structure to extract the base features and an incremental branch equipped with a light-weighted network to capture the temporal dynamics between two adjacent spatiotemporal windows. For enhancing the features, especially in the incremental branch, a point-wise memory bank is designed, which sketches the representative information of event feature space. Compared with the base branch, the incremental branch reduces the computational complexity up to 5 times and improves the speed by 19 times. Experiments show that MENet significantly reduces the computational complexity compared with previous methods while achieving state-of-the-art performance on gesture recognition and object recognition.