In this paper efforts have been made to record the actual, real cost of health care services in a Neonatal Intensive Care Unit (N.I.C.U.) of a public hospital. It is well known that, in recent years, the hospitals have been reimbursed with the system of Diagnosis-Related Groups (D.R.G.’s). The purpose of this study is to determine whether the costs according with D.R.G.’s correspond to the actual-real cost, as this is recorded in the N.I.C.U. This cost is called direct cost. Here is a case study of a premature neonate in the intensive care unit (N.I.C.U.). From the outset, the age of pregnancy, the birth weight, the duration of hospitalization in N.I.C.U. and the needs of the newborn in oxygen, medication, as well as nutrition are defined which are very important in shaping the cost. Then, the cost is calculated according to the D.R.G.’s system. By setting three basic diagnoses (I.C.D.-10), we find the D.R.G. which better describes the case, as well as the associated costs. Then, we calculate the direct cost and list all the consumables, exams, staff costs, overheads. Comparing the two results we find that the cost of D.R.G. does not meet the direct cost of hospitalization. There is a significant deviation from the actual real cost, which proves the under-costing of the health services. The D.R.G.’s system leads hospitals to increase their financial deficits and provide degraded quality health services. It is necessary to readjust the D.R.G.’s according to the reality and the redefinition of the hospital’s reimbursement system to meet the direct – real cost of the health services offered.