Ant-based clustering is a type of clustering algorithm that imitates the behavior of ants. To improve the efficiency, increase the adaptability to non-Gaussian datasets and simplify the parameters of the algorithm, a novel ant-based clustering algorithm using Renyi Entropy (NAC-RE) is proposed. There are two aspects to application of Renyi entropy. Firstly, Kernel Entropy Component Analysis (KECA) is applied to modify the random projection of objects when the algorithm is run initially. This projection can create rough clusters and improve the algorithm s efficiency. Secondly, a novel ant movement model governed by Renyi entropy is proposed. The model takes each object as an ant. When the object (ant) moves to a new region, the Renyi entropy in its local neighborhood will be changed. The differential value of entropy governs whether the object should move or be moveless. The new model avoids complex parameters that have influence on the clustering results. The theoretical analysis has been conducted by kernel method to show that Renyi entropy metric is feasible and superior to distance metric. The novel algorithm was compared with other classic ones by several well-known benchmark datasets. The Friedman test with the corresponding Nemenyi test are applied to compare and conclude the algorithms performance The results indicate that NAC-RE can get better results for non-linearly separable datasets while its parameters are simple.