This paper presents a new approach to constructing a neural tree with partial incremental learning capability. The proposed neural tree, called a quadratic-neuron-based neural tree (QUANT), is a tree structured neural network composed of neurons with quadratic neural-type junctions for pattern classification. The proposed QUANT integrates the advantages of decision trees and neural networks. Via a batch-mode training algorithm, the QUANT grows a neural tree containing quadratic neurons in its nodes. These quadratic neurons recursively partition the feature space into hyper-ellipsoidal-shaped sub-regions. The QUANT has the partial incremental capability so that it does not need to re-construct a new neural tree to accommodate new training data whenever new data are introduced to a trained QUANT. To demonstrate the performance of the proposed QUANT, several pattern recognition problems were tested.