Conceptual cost estimates are important to project feasibility studies, even the final project success. The estimates provide significant information for project evaluations, engineering designs, cost budgeting and cost management. This study proposes an artificial intelligence approach, the evolutionary fuzzy hybrid neural network (EFHNN), to improve precision of conceptual cost estimates. The approach incorporates neural networks (NN) and high order neural networks (HONN) into a hybrid neural network (HNN). The HNN operates with the alternative of linear and non-linear neuron layer connectors. Besides, fuzzy logic (FL) is employed for handling uncertainties, the approach therefore evolve into a fuzzy hybrid neural network (FHNN). For FHNN optimization, the genetic algorithm is used for both FL and HNN, consequently the approach is named as EFHNN. In practical case studies, two estimates including overall and category cost estimates are provided and compared. Results show that the proposed conceptual cost estimates can be deployed as accurate cost estimators during early stages of construction projects. Moreover, considering linear and non-linear neuron layer connectors in EFHNN surpasses models with singular linear deployment of NN.