Nowadays, software development methodologies, such as Rational Unified Process or agile methodologies, recommend developing software by increments instead of following a waterfall lifecycle model. Although Function Points is one of the most known techniques to estimate effort and cost in software projects, there is little work that indicates how to adapt it in non-waterfall lifecycles, such as incremental ones. This paper presents an approach called Incremental-FP that allows estimating effort for each increment using unadjusted function points (UFP) and COCOMO's effort adjustment factor (EAF). This approach could be complemented with the Use Case Precedence Diagram to determine use case prioritization, and the rules proposed in a previous work to count UFP with UML class diagrams. We also present the results by applying our approach in projects with undergraduate students. We obtained good results, because the difference between estimated effort and real effort was lower than 20% for the second increment. Moreover, the results obtained with Incremental-FP were better than the ones obtained with adjusted function points. © 2012 Springer-Verlag.