Tertiary institutions in Nigeria are usually faced with the problem of completing building projects within the scheduled durations and budgeted costs. In this study, 8 building construction projects completed in the Federal Polytechnic of Oil and Gas were analysed between the years 2014 and 2023. A non-linear regression time-cost model was developed based on the Bromilow’s Time-Cost (BTC) model. The results show that it would take 1858.3 working days to complete the construction of a building in a Nigerian tertiary institution for every one million Australian Dollar. Predictions were made for construction durations and construction costs with the formulated model. The model was found to be adequate and fit, with an R 2 value of 0.8218. This also indicates that the BTC model applies to tertiary institution building construction projects in Nigeria.