The success of fuzzy clustering heavily relies on the proper feature space constructed by the input data. For nonspherical and overlapped clusters, kernel fuzzy clustering is more effective because it finds more proper feature space compared to conventional fuzzy clustering. Unfortunately, poor scalability of kernel fuzzy clustering is induced by the construction of a kernel matrix. To solve the problem, random feature-based method was presented to approximate the kernel function. More interestingly, these features exposed in the approximate feature space are directly manipulable. Inspired by the architecture of functional-link neural network, to exploit more information from both the original data space and the approximate kernel space, a new feature space called cascaded feature space (CF) is constructed in this paper. By performing classical fuzzy c-means (FCM) in CF space, a new fuzzy clustering framework called FCM-CF is developed. To reduce computational complexity and perform FCM in CF space well, dimension reduction methods are adopted to generate two variants of FCM-CF. The experiment results of our proposed algorithms verify their superiority in comparison of other classical fuzzy clustering algorithms.