Fibrin networks are a major component of blood clots that provides structural support to the formation of growing clots. Abnormal fibrin networks that are too rigid or too unstable can promote cardiovascular problems and/or bleeding. However, current biological studies of fibrin networks rarely perform quantitative analysis of their structural properties (e.g., the density of branch points) due to the massive branching structures of the networks. In this paper, we present a new approach for segmenting and analyzing fibrin networks in 3D confocal microscopy images. We first identify the target fibrin network by applying the 3D region growing method with global thresholding. We then produce a one-voxel wide centerline for each fiber segment along which the branch points and other structural information of the network can be obtained. Branch points are identified by a novel approach based on the outer medial axis. Cells within the fibrin network are segmented by a new algorithm that combines cluster detection and surface reconstruction based on the α-shape approach. Our algorithm has been evaluated on computer phantom images of fibrin networks for identifying branch points. Experiments on z-stack images of different types of fibrin networks yielded results that are consistent with biological observations.