In this paper, we propose Generalizable and Animatable Gaussian head Avatar (GAGA) for one-shot animatable head avatar reconstruction.Existing methods rely on neural radiance fields, leading to heavy rendering consumption and low reenactment speeds.To address these limitations, we generate the parameters of 3D Gaussians from a single image in a single forward pass.The key innovation of our work is the proposed dual-lifting method, which produces high-fidelity 3D Gaussians that capture identity and facial details.Additionally, we leverage global image features and the 3D morphable model to construct 3D Gaussians for controlling expressions.After training, our model can reconstruct unseen identities without specific optimizations and perform reenactment rendering at real-time speeds.Experiments show that our method exhibits superior performance compared to previous methods in terms of reconstruction quality and expression accuracy.We believe our method can establish new benchmarks for future research and advance applications of digital avatars.