By using Sb2Te3 nanosheets as saturable absorbers (SA) and an acousto-optic modulator (AOM), a laser-diode (LD) end-pumped idler-resonant KTiOAsO4 (KTA)-based intracavity optical parametric oscillator (IOPO) pumped by a dual-loss-modulated Q-switched mode-locked (QML) laser has been realized. The experimental results show that the pulse widths of the Q-switched envelope and the mode-locking pulse numbers underneath the Q-switched envelope decrease as the pump power increases. When the pump power reaches a certain value, only one mode-locking pulse underneath a Q-switched envelope exists, resulting in the generation of the subnanosecond mode-locking pulses of OPO with the repetition rate of AOM. The minimum mode-locking pulse durations of the signal and idler waves were measured to be 545 and 936 ps at an AOM frequency of 1 kHz and a diode pump power of 22.45 W, corresponding to the maximum peak powers of 648 and 185 kW, respectively. Furthermore, a set of coupled rate equations for the dual-loss-modulated QML laser-pumped intracavity idler-resonant OPO was formulated according to the Gauss distribution of intracavity photon density. The numerical simulations of these equations agree with the experimental results. These results collectively suggest the potential application of Sb2Te3 as a promising nanomaterial in the realm of optoelectronics.