A Construction Project Management involves initiating, planning, evaluating/monitoring, controlling and closing out a project for optimal time and minimum cost. So Construction Project Management is the overall coordination of these management processes from beginning to completion of the construction project. In construction projects, time and cost are the most important factors to be considered during scheduling. The aim of this study is to develop an optimization model that finds a best solution of the trade-off between time and cost to expedite the execution process in order to complete the project with optimum duration and with minimum cost at a time. Critical path method (CPM) is used to determine the longest duration and cost required for completing of the project and then the time-cost trade–off problem (TCTP) is formulated as a linear programming model. The model was applied in a hypothetical study area and validated by using practical data collected from the case study. The developed model has been solved by using Microsoft Excel solver for mathematical simplification. The case study is conducted on 3B + G + 7 Mayor Office building construction project located in Debre Markos town which is under construction. The scheduled data has been collected from the project management office. Some additional data which are relevant to carry out the study has been collected by interviewing project manager. Consequently, the project activities have been scheduled by the developed LP models for their validity and practicability in the real construction projects. The total costs of the selected activities are reduced from $65000 to $61600 and 403,524 to 401,950 birr which has a reduction of 5.2% & 0.4 %, in hypothetical study and practical case study, respectively. Furthermore, the duration of the project is reduced from 10 days to 8 days and 22 days to 17 days which reduced by 20 % & 22.7 % in case study and hypothetical example, respectively. The linear programming model presented in this study determines effectively by how much the duration for each activity of the project should be crashed for optimum time cost trade-off. The objective function of the LP model and constraints are effectively determined. It was also very important to have an understanding of the trade-off between cost and time. This approach is very important to real cause problems for the optimal use of both time and cost trade off in the construction projects.