Prediction of the South Asian summer monsoon (SASM) has remained a challenge for both scientific research and operational climate prediction for decades. By identifying two dominant modes of the SASM, we show that the unsatisfactory prediction may be due to the fact that the existing SASM indices are mostly related to the less predictable second mode. The first mode, in fact, is highly predictable. It is physically linked to the variation of the Indian monsoon trough coupled with large rainfall anomalies over core monsoon zone and the northern Bay of Bengal. An index is constructed as a physical proxy of this first mode, which can be well predicted one season in advance, with an overall skill of 0.698 for 1979-2020. This result suggests a predictable prospect of the SASM, and we recommend the new index for real-time monitoring and prediction of the SASM.