The Gaussian beam theory has been developed to describe the power characteristics of the steady-state operating ring cavity singly resonant optical parametric oscillator (SRO) with intracavity optical amplification (ICOASRO). The threshold of SRO can be greatly lowered with suitable parameters of the optical amplifier. Under the mean-field approximation, there are four operating domains for a ICOASRO without the second-order nonlinear coupling, meanwhile there exits a minimum pump threshold for the SRO. The characteristics of the end-pumped laser gain medium used as optical amplifier is considered. The generalized characteristics of SRO are also considered in the derivation.