The small-scale self-focusing of divergent beams is studied. Based on the nonlinear paraxial wave equation, the propagation equation of small-scale perturbation of divergent beams has been deduced with a coordinate transformation. The evolvement law of the growth critical frequency of small-scale perturbation, maximum growth frequency and relative B integral is obtained. The influence of the initial radius of divergent beams on small-scale self-focusing is discussed. It is found that for a given propagation distance, the fastest growing frequency, the maximum perturbation growth, and thus the B integral decrease with the decrease of the initial radius of divergent beams. For a given initial radius, as the propagation distance increases, the growth of the B-integral becomes slow and stops at last. Also, the expression for the distance at which the filaments are formed is obtained by local energy conservation, and it is shown that a small initial radius extends the filamentation distance.