This study introduces a progressive neural network (PNN) model for direction of arrival (DOA) estimation, DOA-PNN, addressing the challenge due to catastrophic forgetting in adapting dynamic acoustic environments. While traditional methods such as GCC, MUSIC, and SRP-PHAT are effective in static settings, they perform worse in noisy, reverberant conditions. Deep learning models, particularly CNNs, offer improvements but struggle with a mismatch configuration between the training and inference phases. The proposed DOA-PNN overcomes these limitations by incorporating task incremental learning of continual learning, allowing for adaptation across varying acoustic scenarios with less forgetting of previously learned knowledge. Featuring task-specific sub-networks and a scaling mechanism, DOA-PNN efficiently manages parameter growth, ensuring high performance across incremental microphone configurations. We study DOA-PNN on a simulated data under various mic distance based microphone settings. The studies reveal its capability to maintain performance with minimal parameter increase, presenting an efficient solution for DOA estimation.