This paper tackles problems encountered in mining of incomplete data for knowledge discovery of construction databases. As historical construction data are expensive to collect, any waste of incomplete data means not only loss of knowledge but also increase of costs for knowledge discovery of construction engineering. Unfortunately, incompleteness is commonplace in the existing construction databases. This paper proposes a VaFALCON (Variable-Attribute Fuzzy Adaptive Logic Control Network) neuro-fuzzy system that is equipped with the power for mining incomplete historical data. The proposed VaFALCON is shown to successfully mining of construction data with various percentages of missing attribute values.