We demonstrate a pulsed mid-infrared (MIR) optical parametric oscillator (OPO) with both inter-pulse and intra-pulse dual-wavelength operation capability. A fiber master oscillator power amplifier incorporating an acousto-optic tunable filter (AOTF) was employed as the pump for the OPO. By finely adjusting the drive wave packets for the AOTF, dual-wavelength pump can be realized within each pulse or between two adjacent pulses. These special temporal-spectral behaviors of the pump can be transferred to MIR via an OPO. In the proof-of-principle experiments, two pump wavelengths at ∼1065 and ∼1076 nm were generated and amplified to ∼31.2 W with equivalent spectral intensities for both pulsation modes. At the highest pump power, total idler power of ∼3.5 W was achieved at ∼3.45 and ∼3.55 µm under both pulsation modes. To the best of our knowledge, this is the first demonstration of both inter-pulse and intra-pulse dual-wavelength MIR generation via an OPO with an identical configuration. It is believed that our design may provide a promising solution to many practical applications including differential absorption lidar and tunable terahertz wave generation.