Kernel clustering methods are useful to discover the non-linear structures hidden in data, but they suffer from the difficulty of kernel selection and high computational complexity. In this paper, we propose a novel random feature map-based multiple kernel fuzzy clustering method with all feature weights, in which low-rank randomized features of multiple kernels are generated by random Fourier feature map and Quasi-Monte Carlo feature map, and maximum entropy technique is applied to optimize the weights of all feature attributes. The proposed method is effective to extract important kernel and the important attributes of the kernel so as to achieve good clustering results. What is more, compared with conventional kernel clustering methods, our method is much more time-saving and is available to large data sets. The experiments based on various data sets show the superiority and efficiency of the proposed method.