A kind of discounted problems for singular diffusion control have been studied.The drift and diffusion coefficients of state process are nonlinear.The class of models has been basically extended from a corresponding one established by Karatzes et al.before.By applying some analysis methods different from earlier works,the sufficient and necessary conditions of the existence of optimal control have been obtained.If an optimal control exists,it is a "transient reflection" of state process for two lines.