The segmentation of cells and neurites in microscopy images of neuronal networks provides valuable quantitative information about neuron growth and neuronal differentiation, including the number of cells, neurites, neurite length and neurite orientation. This information is essential for assessing the development of neuronal networks in response to extracellular stimuli, which is useful for studying neuronal structures, for example, the study of neurodegenerative diseases and pharmaceuticals. However, automatic and accurate analysis of neuronal structures from phase contrast images has remained challenging. To address this, we have developed NeuroQuantify, an open-source software that uses deep learning to efficiently and quickly segment cells and neurites in phase contrast microscopy images. NeuroQuantify offers several key features: (i) automatic detection of cells and neurites; (ii) post-processing of the images for the quantitative neurite length measurement based on segmentation of phase contrast microscopy images, and (iii) identification of neurite orientations. The user-friendly NeuroQuantify software can be installed and freely downloaded from GitHub https://github.com/StanleyZ0528/neural-image-segmentation.