Optical-resolution photoacoustic microscopy (OR-PAM) has been shown to be an excellent tool for high-resolution imaging of microvasculature, and quantitative analysis of the microvasculature can provide valuable information for the early diagnosis and treatment of various vascularrelated diseases. In order to address the characteristics of weak signals, discontinuity and small diameters in photoacoustic microvascular images, we propose a method adaptive to the microvascular segmentation in photoacoustic images, including Hessian matrix enhancement and the morphological connection operators. The accuracy of our vascular segmentation method is quantitatively evaluated by the multiple criteria. To obtain more precise and continuous microvascular skeletons, an improved skeleton extraction framework based on the multistencil fast marching (MSFM) method is developed. We carried out in vivo OR-PAM microvascular imaging in mouse ears and subcutaneous hepatoma tumor model to verify the correctness and superiority of our proposed method. Compared with the previous methods, our proposed method can extract the microvascular network more completely, continuously and accurately, and provide an effective solution for the quantitative analysis of photoacoustic microvascular images with many small branches.