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Many biological fibrous tissues exhibit distinctive mechanical properties arising from their highly organized fibrous structure. In disease conditions, alterations in the primary components of these fibers, such as type I collagen molecules in bone, tendons, and ligaments, assembly into a disorganized fibers architecture generating a weak and/or brittle material. Being able to quantitatively assess the fibers orientation and organization in biological tissue may help improve our understanding of their contribution to the tissue and organ mechanical integrity, and assess disease progress and therapy effect. In this work, we present FiberO, a new open-source available software that automatically quantifies fibers orientation, by performing morphological image openings, and fibers organization within the tissue, by determining and plotting their continuity in groups. FiberO performance is here evaluated using second harmonic generation microscopy images of mouse bones and tendons as examples of biological fibrous tissues. FiberO outperformed Directionality and OrientationJ, two open-source plugins available in ImageJ, and FiberFit and CT-FIRE, in the calculation and plotting of fibers orientation in reference images with known fibers orientation. Additionally, FiberO is currently the sole software to date able to accurately track the continuity of aligned fibers, and it quantifies and displays the organized surface(s) in the tissue of interest. FiberO can be used in the wider engineering and science field to investigate the fibers orientation and organization of different natural and synthetic fibrous tissues.