This paper is submited for publication on IEEE Transcations for Neural Networks and Learning System (ID: TNNLS-2016-P-6504) This paper presents a novel online adaptive neuro-computing framework for a robust time-series forecast. The proposed framework does mimic the human mind's biological two-thinking model. Our mind makes decisions/calculations using a two-connected system. A first system, System 1, the so-called the intuitive system, makes decisions based on our experience. A second system, System 2, the controller system, does control the decisions of System 1 by either modifying or trusting them. Similarly to the human mind's two-systems model, this paper proposes an artificial framework consisting of two cellular neural network (CNN) systems. The first CNN processor does represent the intuitive system and we call it Intuitive-CNN. The Second CNN processor does represent the controller system, which is called Controller-CNN. Both are connected within a general framework that we name OSA-CNN. The proposed framework is extensively tested, validated and benchmarked with the best state-of-the-art related methods, while involving real field time-series data. Multiple scenarios are considered: traffic flow data extracted from the PeMs traffic database and the 111 time-series collected from the so-called NN3 competitions. The novel OSA-CNN concept does remarkably highly outperform the state-of-the-art competing methods regarding both performance and universality. Index Terms—Time-series forecast (TFS), Cellular neural networks (CNN), Echo state network (ESN), Model reference neural network adaptive control (MRNNAC), Recursive particle swarm optimization (RPSO), Online self-adaptive CNN (OSA-CNN)