A continuous-wave, tandem optical parametric oscillator (TOPO) based on a MgO-doped periodically poled LiNbO3 (MgO:PPLN) is demonstrated. Because the MgO:PPLN is tandemly pumped by the OPO’s signal beam, it outputs simultaneously two groups of signal and idler with a single pump source. The entire range spans from 1398 to 1490 nm, 1914 to 2107 nm, 3720 to 4444 nm, and 4849 to 5190 nm, which is limited by periods of the MgO:PPLN and cavity mirror coatings. The TOPO, whose oscillation threshold of pump power exceeds 7 W, can be easily triggered by marginally increasing the pump power as long as the OPO process occurs. The maximum idler powers are respectively 2.6 W (at 3896 nm) and 34 mW (at 4863 nm), and the corresponding signal powers are both nearly 100 mW.