The introduction of 3D Gaussian blendshapes has enabled the real-time reconstruction of animatable head avatars from monocular video. Toonify, a StyleGAN-based method, has become widely used for facial image stylization. To extend Toonify for synthesizing diverse stylized 3D head avatars using Gaussian blendshapes, we propose an efficient two-stage framework, ToonifyGB. In Stage 1 (stylized video generation), we adopt an improved StyleGAN to generate the stylized video from the input video frames, which overcomes the limitation of cropping aligned faces at a fixed resolution as preprocessing for normal StyleGAN. This process provides a more stable stylized video, which enables Gaussian blendshapes to better capture the high-frequency details of the video frames, facilitating the synthesis of high-quality animations in the next stage. In Stage 2 (Gaussian blendshapes synthesis), our method learns a stylized neutral head model and a set of expression blendshapes from the generated stylized video. By combining the neutral head model with expression blendshapes, ToonifyGB can efficiently render stylized avatars with arbitrary expressions. We validate the effectiveness of ToonifyGB on benchmark datasets using two representative styles: Arcane and Pixar.