Contract award and its management is a fundamental task in the execution of public construction projects in the construction industry. In Ethiopia, public-owned construction projects mostly used the least cost contract award system as a procurement and contract approach but it was traditional. Hence, the benefit of the contract award system should show effective performance with respect to the three construction parameters; cost, quality, and time. Different research was conducted to address the challenges of improving the contract award method, there is still a gap in improving contract approaches. Thus, the researcher came up with a research problem in the practice of the least cost contract in public building construction projects. The objective of this study is to investigate the practice of least cost contract and design a framework for the contract award system by taking public building construction projects in Bahir Dar city as a case study. The study adopted a questionnaire survey, interview, and case study research methodology to collect data from construction stakeholders involved in public projects with main participants including clients, contractors, and consultants. The study also analyzed the collected data using the average index of the Likert scale, Microsoft-excel, and SPSS application. The study finding indicated that the least cost contract of public building construction projects in Bahir Dar city was inadequately performed for the effective accomplishment of project cost, time, and quality parameters and different factors affecting the effective implementation of the least cost contract system were identified. As a result, the thesis found out low performance during execution and lest cost contract award system was the impact of the current contract awarding approach in public building construction projects. In line with this, the practice of other contract approach was investigated with respect to the current contract approach. Thus, the investigation of a conceptual contract award framework adaptation in public building construction project was a mandate to the effective achievement of project parameters.