In this paper, the definition of information entropy of Smoluchowski coagulation equation for Brownian motion is introduced based on coagulation probability. The expression of entropy is the function of geometric average particle volume and standard deviation with lognormal distribution assumption. The asymptotic solution with moment method shows that the entropy is a monotone increasing function of time, which is equivalence to the entropy based on particle size distribution. the result reveals that the present definition of entropy of Smoluchowski coagulation equation are inadequate because the particle average volume at equilibrium cannot be determined from the principle of maximum entropy. This provides a basis for further exploring the global properties of Smoluchowski coagulation equation.