Accurate prediction of the Asian-Australian monsoon (A-AM) seasonal variation is one of the most important and challenging tasks in climate prediction. In order to understand the causes of the low accuracy in the current prediction of the A-AM precipitation, this study strives to determine to what extent the ten state-of-the-art coupled atmosphere-ocean-land climate models and their multi-model ensemble (MME) can capture the two observed major modes of A-AM rainfall variability–which account for 43% of the total interannual variances during the retrospective prediction period of 1981–2001. The first mode is associated with the turnabout of warming to cooling in the El Niño-Southern Oscillation (ENSO), whereas the second mode leads the warming/cooling by about 1 year, signaling precursory conditions for ENSO. The first mode has a strong biennial tendency and reflects the Tropical Biennial Oscillation (Meehl in J Clim 6:31–41, 1993). We show that the MME 1-month lead prediction of the seasonal precipitation anomalies captures the first two leading modes of variability with high fidelity in terms of seasonally evolving spatial patterns and year-to-year temporal variations, as well as their relationships with ENSO. The MME shows a potential to capture the precursors of ENSO in the second mode about five seasons prior to the maturation of a strong El Niño. However, the MME underestimates the total variances of the two modes and the biennial tendency of the first mode. The models have difficulties in capturing precipitation over the maritime continent and the Walker-type teleconnection in the decaying phase of ENSO, which may contribute in part to a monsoon “spring prediction barrier” (SPB). The NCEP/CFS model hindcast results show that, as the lead time increases, the fractional variance of the first mode increases, suggesting that the long-lead predictability of A-AM rainfall comes primarily from ENSO predictability. In the CFS model, the correlation skill for the first principal component remains about 0.9 up to 6 months before it drops rapidly, but for the spatial pattern it exhibits a drop across the boreal spring. This study uncovered two surprising findings. First, the coupled models’ MME predictions capture the first two leading modes of precipitation variability better than those captured by the ERA-40 and NCEP-2 reanalysis datasets, suggesting that treating the atmosphere as a slave may be inherently unable to simulate summer monsoon rainfall variations in the heavily precipitating regions (Wang et al. in J Clim 17:803–818, 2004). It is recommended that future reanalysis should be carried out with coupled atmosphere and ocean models. Second, While the MME in general better than any individual models, the CFS ensemble hindcast outperforms the MME in terms of the biennial tendency and the amplitude of the anomalies, suggesting that the improved skill of MME prediction is at the expense of overestimating the fractional variance of the leading mode. Other outstanding issues are also discussed.