The newly proposed Taylor-expansion moment method (TEMOM) is extended to solve agglomerate coagulation in the free-molecule regime and in the continuum regime, respectively. The moment equations with respect to fractal dimension are derived based on 3rd Taylor-series expansion technique. The validation of this method is done by comparing its result with the published data at each limited size regime. By comparing with analytical method, sectional method (SM) and quadrature method of moments (QMOMs), this new approach is shown to produce the most efficiency without losing much accuracy. At each limited size regime, the effect of fractal dimension on the decay of particle number and particle size growth is mainly investigated, and especially in the continuum regime the relation of mean diameters of size distributions with different fractal dimensions is first proposed. The agglomerate size distribution is found to be sensitive to the fractal dimension and the initial geometric mean deviation before the self-preserving size distribution is achieved in the continuum regime. (C) 2009 Elsevier Inc. All rights reserved.