Idiopathic infantile arterial calcification (IIAC), also known as generalized arterial calcification of infancy (GACI), is a heritable ectopic mineralization disorder that results in diffuse arterial calcifications and or stenosis, which are attributed to mutations in the ENPP1 gene. In this case study, we report the development of IIAC in a 2-month-old male preterm infant. The patient presented with severe hypertension and seizures, which revealed diffused calcifications and c.130C > T and c.1112A > T mutations in the ENPP1 gene. With biphosphonate, antihypertensive, and control epilepsy therapy, his blood pressure was maintained at 110-120/50-60 mmHg. Intellectual motor development retardation was anticipated in this patient. To the best of our knowledge, this is the first case in which a novel c.130C > T mutation in the ENPP1 gene has been identified, and the administration of bisphosphonates to patients with IIAC has been assessed.