Hydrogel-based biomedical applications are under rapid development. These applications usually demand hydrogels to have high toughness and high fatigue threshold. Recently, various fiber-reinforced composite hydrogels have been developed to meet this challenge. However, the effect of fiber geometry on the fracture and fatigue of composite hydrogels is still elusive. Here, we use a model composite hydrogel to study the influence of fiber width, fiber spacing, and fiber configuration on these properties. It is found that the toughness of the composite hydrogel does not increase monotonically with the fiber width or fiber spacing, but presents a peak. This is because the variation of fiber width and fiber spacing not only affects the volume of fiber in the fracture process zone but also influences the dissipated elastic energy density in that volume, which is affected by the stress concentration. The peak is a consequence of the trade-off between these two factors. Our study further shows that the shape of the fiber network affects the stress concentration in the fiber dramatically, thereby leading to a huge difference in the toughness and fatigue threshold of the composite hydrogels. This work highlights the importance of fiber size as well as the shape of fiber networks on the mechanical properties of composite hydrogels. It may help the design of tough and fatigue-resistant stretchable composite materials.