In this work, we explore 2D Gaussian splat as a new primitive for representing and compressing videos, showing its promise as an alternative to traditional signal-based primitives. We introduce GSVC, a new Gaussian splatting-based video codec that incorporates common techniques used in classical video codecs to exploit temporal redundancy between nearby frames. In GSVC, each frame is represented by a set of overlapping Gaussian splats, which, when rendered together, approximate the original frame. Gaussian splats for the first frame and subsequent frames following scene changes (called anchor frames) are learned from scratch, while the remaining frames (called propagation frames) are initialized from the Gaussian splats of their previous frames and then fine-tuned. Scene changes are detected through loss differences during the training process. To capture large motion or newly appeared objects, we randomly add Gaussian splats to propagation frames before fine-tuning. GSVC supports a knob for rate-distortion trade-offs through controlling the number of Gaussian splats for each frame. Gaussian splats with low contributions to the frame quality can be removed during training. GSVC supports two-pass encoding by propagating the Gaussian splats from a future propagation frame back to an anchor frame, further improving the video quality for challenging video scenes. To achieve efficient compression, GSVC uses a residual-based Gaussian splats quantization framework that encodes only changes to the Gaussian parameters between frames. Experimental results show that GSVC achieves rate-distortion performance comparable to state-of-the-art video codec implementations for AV1 and VVC. GSVC inherits the advantages of Gaussian splatting in rendering, allowing it to achieve the rendering speed of 1500 fps for a 1920 × 1080 video.