Large cupping of the optic disk in a baby or a child can be indicative of primary congenital glaucoma. Primary congenital glaucoma is often refractory to treatment, and lifelong management and follow-up are necessary; therefore, diagnosis requires careful consideration. In this study, we describe the case of twins in whom primary congenital glaucoma was initially suspected due to large cupping of the optic disks. Twin babies (a boy and a girl weighing 455 g and 592 g respectively), born prematurely (at 28 gestational weeks), were referred to our hospital eight months after birth because large cupping of the optic disks was detected during follow-up for retinopathy of prematurity. According to color fundus photographs, the cup/disk ratios in both eyes of both babies ranged from 0.75 to 0.86. However, the axial length ranged from 18.57 to 19.91 mm, the anterior chamber depth ranged from 2.68 to 2.93 mm, and the horizontal diameters of the corneas, which were clear, ranged from 10 to 10.5 mm. The intraocular pressures (IOPs), as measured by a rebound tonometer, were 15.3-19.7 mmHg. Glaucoma was strongly suspected due to the large cupping of the optics disks; however, other ocular biometric tests demonstrated that the eyes were normal. After eight months of follow-up without any medication or intervention, the IOPs stabilized between 6-22.1 mmHg, the refractive errors were between -2.5 and 0 diopters, and we found no apparent enlargement of the optic disks. In addition, we investigated both parents’ optic disks to evaluate the genetic factors and found that they had relatively large C/D ratios (0.68-0.79). These premature twins exhibited glaucoma-like optic disks with large cupping, but no solid glaucomatous changes were observed with ocular biometry and IOP testing. We concluded, therefore, that the early birth and lower birth weights may have been associated with the large cupping of the patients’ optic disks. To differentiate between normal physiological cupping and primary congenital glaucoma, ocular morphological examination of the eye, IOP measurements, and investigation of the parents’ optic disks were useful.