In this study, we extend the Taylor-series expansion method of moment to two-component aggregation problem undergoing Brownian coagulation with kernels that are independent of composition. A set of closed particle population balance equation for lower-order moments is then derived. Numerical results and its asymptotic solutions are validated by comparing with Monte Carlo simulation method both in free molecular regime and continuum regime. It is shown that three dimensionless particle moments M-C1, M-C2, M-C3 almost approach to a same value over large evolution time. The normalized variance of excess component A decreases as 1/(nu) over bar and it tends to zero over large evolution time.