In this study, one of the most promising methods of tailoring a composite scaffold material in nanosized diameters, electrospinning method were used to fabricate polycaprolactone (PCL)/graphene oxide (GO)/iron(II, III) oxide (Fe3O4) nanocomposite fibers as biocompatible scaffolds for biomedical applications. The prepared nano-fibers were characterized using the scanning electron microscopy. Grayscale scanning electron microscopy images of composite nanofibers were analyzed by a new image analysis procedure for determination of fibers diameter, diameter distribution, orientation of nanofibers and the compactness of electrospun nanofibers. The developed image analysis procedure consists of three phases, preprocessing phase, morphological operation phase and feature extraction phase. In first phase, preprocessing methods are applied to enhance scanning electron microscopy images. After preprocessing phase, grayscale images are converted into binary images. In second phase, morphological operations such as erosion, dilation are applied on binary regions. Then, region of interests are detected on binary images. In the feature extraction phase, morphological features are extracted and calculated from region of interests.