Abstract: The clustering methods can exactly describe clustering criterion with formulations by the objective function. The classification problem can be better solved. In comparison with the representative fuzzy C means （FCM） algorithm, the advantage of the g λ clustering algorithm （GLCA） is that the selection of weighting exponent is not required and it extends the probability density to the fuzzy measure. In the paper here the convergence analysis of the g λ clustering algorithm is conducted, the divergence of the g λ clustering algorithm is proved, and the non convergent example is presented.