The government had mainly provided health delivery in Ghana; this did not leave room for so much client (patient) specifications and demand. Recent times have however seen the emergence of some private entities delivering health care, bringing in some form of competition in the sector. The purpose of this study was to assess client satisfaction with service delivery in the health sector. The study specifically sought to determine the factors that are associated with satisfaction of the patients in the hospital, to find out patients' knowledge of the right to demand and expect service quality or satisfaction, to determine the impact of some service dimensions on patients' satisfaction and to identify the challenges that impact on satisfactory service delivery at the hospital. The population comprised both staff and patients of Agogo Presbyterian hospital. Through convenience sampling, 151 patients and 51 staff were sampled. Data was analyzed using basic descriptive statistics. Multiple regression analysis and correlation was also used to ascertain the effect of the independent variables (human relation of staff, communication from staff, staff performance, waiting time and physical evidence) and the dependent variable (patients' satisfaction). It was concluded that, patients were satisfied with the health service delivery at Agogo Presbyterian hospital. Factors that led to satisfaction were effective human relation from staff (doctors, pharmacists, nurses and other staff), effective communication and general performance of staff. It has therefore been suggested that the facility must take keen interest in them, so as to enhance the satisfaction of their patients.