We have carried out a close examination on the mathematical treatments and the first-principle computations concerning the vibronic transitions between the S(0)(1)A(1) and the S(1)(1)A(2) states of formaldehyde. The simulation of absorption spectrum was presented with peak intensities calculated according to vibronic-coupled transition dipole moments and Franck-Condon factors. The radiative and non-radiative transition rate constants from the excited to the ground states were calculated with formulas based on Fermi's golden rule. It is concluded that our simulated absorption spectrum between 300 and 360 nm, as well as the estimated relaxation rate constants, showed good agreements with experimental reports.