The association ability of neural networks composed of chaotic neuron models or chaotic neuron-based models are very sensitive to chaotic neuron parameters such as scaling factor of refractoriness α and damping factor k and so on. And, in these models, appropriate parameters have to determined by trial and error. In this research, a Chaotic Multidirectional Associative Memory with adaptive scaling factor of refractoriness which can realize one-to-many associations and whose parameters can be determined automatically is proposed. In this model, scaling factor of refractoriness α varies depends on time and internal states of neurons. We examined one-to-many associations ability of the proposed model and the Chaotic Multidirectional Associative Memory with variable scaling factor of refractoriness. And, we confirmed that one-to-many association ability of the proposed model is almost equal to that of well-tuned Chaotic Multidirectional Associative Memory with variable scaling factor of refractoriness.