Propagation of PAMAM (polyamidoamine) dendrons on solid spherical silica gel was achieved by a series of alternate Michael addition and amidation reactions. The reaction kinetics studies were investigated quantitatively. A newly developed method of immobilizing inert 3-(triethoxysilyl) propionitrile (TESPN) on silica before construction of PAMAM dendrons provided an internal standard to normalize drift IR spectra for kinetics studies. A reaction kinetic model was proposed on the basis of IR spectra and TGA measurements. The simulated results match with the experimental data and confirm consistency with the proposed kinetic model that a "cross-linking" reaction occurred in amidation generating structural defects, and steric hindrance existed during the Michael addition reaction. Furthermore, we found that the TESPN immobilized on silica acted as a "spacer" to reduce the initial density of amino groups on silica and improved the synthesis efficiency remarkably. The reaction kinetics study in this paper is instrumental to the optimization of the synthesis of PAMAM dendrons on solid surface.