Unravelling the volcanic history of the enigmatic lunar farside is essential for understanding the hemispheric dichotomy of the Moon1-3. Cratering chronology established for the lunar nearside has been used to suggest long-lived volcanism on the farside of the Moon3,4, but without sample verification. Here we report two newly recognized episodes of basaltic volcanism with Pb-Pb dating for basalt fragments returned by the Chang’e-6 mission. One high-Al basalt fragment dated at 4,203 ± 4 million years ago (Ma) has a source 238U/204Pb ratio (µ value) of ~1,620, implying a KREEP-rich (K, rare earth elements, and P) source for this oldest-known occurrence of basaltic volcanism among returned samples. The main volcanic episode of the Chang’e-6 basalt documents a surprisingly young eruption age of 2,807 ± 3 Ma, which is not recognized from the nearside of the Moon. The initial Pb isotope compositions of these younger basalts indicate derivation from a source with a µ value of ~360, indicating a KREEP-poor mantle source. Mare volcanism on the lunar farside thus persisted for >1.4 billion years even with a shift to a source depleted in heat-producing elements. The consistency between the 2.8-billion-year basalt age and its crater-counting age indicates that the cratering chronology model established for the lunar nearside is also applicable to the farside of the Moon.