Creating high-fidelity and editable head avatars is a pivotal challenge in computer vision and graphics, boosting many AR/VR applications. While recent advancements have achieved photorealistic renderings and plausible animation, head editing, especially real-time appearance editing, remains challenging due to the implicit representation and entangled modeling of the geometry and global appearance. To address this, we propose Surface-Volumetric Gaussian Head Avatar (SVG-Head), a novel hybrid representation that explicitly models the geometry with 3D Gaussians bound on a FLAME mesh and leverages disentangled texture images to capture the global appearance. Technically, it contains two types of Gaussians, in which surface Gaussians explicitly model the appearance of head avatars using learnable texture images, facilitating real-time texture editing, while volumetric Gaussians enhance the reconstruction quality of non-Lambertian regions (e.g., lips and hair). To model the correspondence between 3D world and texture space, we provide a mesh-aware Gaussian UV mapping method, which leverages UV coordinates given by the FLAME mesh to obtain sharp texture images and real-time rendering speed. A hierarchical optimization strategy is further designed to pursue the optimal performance in both reconstruction quality and editing flexibility. Experiments on the NeRSemble dataset show that SVG-Head not only generates high-fidelity rendering results, but also is the first method to obtain explicit texture images for Gaussian head avatars and support real-time appearance editing.