These research asses the customer satisfaction related with five dimensions of service quality (tangibility, reliability, responsiveness, assurance and empathy) in one of the private bank Birhan International Bank branches found in Mekelle. Customer satisfaction is defined as meeting of customer thought and the firm delivery of the service. And service quality has been defined as one of the most important dimension that customers use to differentiate between services offered by different companies. To achieve the objective of the study, data was collected through questioners from the sample of48 customers of the bank. These respondents were selected using convenience sampling technique. The data collected from the questionnaires were analyzed using descriptive tools such as mean, percentage, table and frequency distribution analysis and the result of the study indicate that except empathy therefore service quality dimensions (tangibility, assurance, reliability, and responsiveness) have positive effect on customer satisfaction. The finding of the study also indicates that customers were not satisfied with the empathy dimension of service quality.