That the fuzzy index m must be larger than I can guarantee the convergence of the fuzzy clustering algorithm, however, it also restricts the universality of the clustering algorithm. We propose a novel clustering algorithm called the general multivariable fuzzy C-means clustering (GMFCM). Based on multivariable fuzzy C-means clustering (MFCM), the particle swarm optimization algorithm (PSO) is used to perform the optimization estimation on the fuzzy memberships of the GMFCM, thus the scope of the fuzzy index m is extended to m>0, and the iterative formula of clustering center is derived by the gradient method for the GMFCM. We prove the thereom of new m value scope theoretically and discuss the convergence of the GMFCM. The GMFCM removes the restriction of the fuzzy clsutering on m, and makes up the incompleteness of the MFCM algorithm when the clustering center components and the sample components overlap. Simulation experiments prove the effectiveness of the GMFCM.