Creating photorealistic and animatable 3D head avatars across multiple views is still an ongoing challenge in AR/VR applications. Although previous studies adopt Neural Radiance Fields (NeRF) with 3D Morphable Model (3DMM) as a prior to produce impressive results in generating 3D heads, they incur considerable time costs and lack rendering quality. In this paper, we propose a novel approach called MGHead that synthesizes high-fidelity dynamic 3D head avatar with realistic appearance and complex deformation. It exploits anchor-based 3D Gaussians to model geometric shape and extends the fundamental deformation structure of a parametric morphable face model to each fixed point, providing greater robustness in responding to expressive variations. Notably, we introduce an expression and pose-dependent attribute adapter that injects driving signals into anchor features to refine neural Gaussian attributes. This adjustment compensates for the deficiencies of linear blend skinning in capturing high-frequency dynamics effectively, further improving the expressive realism and natural appearance of head avatar. Extensive experiments demonstrate the superiority of our model in visual detail quality and quantitative evaluations.