Traditional kernel-based fuzzy clustering helps to discover the complex structures hidden in data, but it suffers from high computational complexity. This paper introduces random Maclaurin feature (RMF) into fuzzy clustering, and proposes a random Maclaurin feature-based fuzzy clustering algorithm (RMFCM). In this method, the RMF is used to approximate polynomial kernel, and the fuzzy clustering with linear computational complexity is conducted in generated feature space. The experiments carried out on four synthetic datasets and four UCI real-world datasets prove the effectiveness and efficiency of the proposed RMFCM method. The influence of the dimension of the RMF is also studied in the experiments.