Handwritten text generation (HTG) aims to synthesize handwritten samples by imitating a specific writer, which has a wide range of applications and thus has significant research value. However, current studies on HTG are confronted with a main bottleneck: dominant models lack the ability to perceive and integrate handwriting styles, which affects the realism of the synthesized samples. In this paper, we propose GL-GAN, which effectively captures and integrates global and local styles. Specifically, we propose a Hybrid Style Encoder (HSE) that combines a state space model (SSM) and convolution to capture multilevel style features through various receptive fields. The captured style features are then fed to the proposed Dynamic Feature Enhancement Module (DFEM), which integrates these features by adaptively modeling the entangled relationships between multilevel styles and removing redundant details. Extensive experiments on two widely used handwriting datasets demonstrate that our GL-GAN is an effective HTG model and outperforms state-of-the-art models remarkably. Our code is publicly available at:https://github.com/Fyzjym/GL-GAN.