Through applying the Taylor-expansion technique to the particle general dynamic equation, the newly proposed Taylor-expansion moment method (TEMOM) is extended to solve agglomerate coagulation due to Brownian motion in the entire size regime. The TEMOM model disposed by Dahneke's solution (TEMOM-Dahneke) is proved to be more accurate than by harmonic mean solution (TEMOM-harmonic) through comparing their results with the reference sectional model (SM) for different fractal dimensions. in the transition regime, the TEMOM-Dahneke gives the more accurate results than the quadrature method of moments with three nodes (QMOM3). The mass fractal dimension is found to play an important role in determining the decay of agglomerate number and the spectrum of agglomerate size distribution, but the effect decreases with decreasing agglomerate Knudsen number. The self-preserving size distribution (SPSD) theory and linear decay law for agglomerate number are only applicable to be in the free molecular regime and continuum plus near-continuum regime, but not perfectly in the transition regime. (C) 2009 Elsevier Ltd. All rights reserved.