In this paper, the weakest bound electron potential model (WBEPM) theory is employed to study the transition probability of many-valence-electron systems Cu I, Ag I, and Au I. According to this theory, a coupled equation is used to obtain the parameters Z*, n*, and l*, which are needed in the calculation of transition probability. In the calculation, spectral fine structure is taken into consideration, and node numbers of silver and gold are adjusted. Compared with the accepted values, the results reported here are fairly good, and agreement is within the uncertainty of the accepted values. In our discussion, we give the explanation of node number adjustment from the view of WBEPM theory.