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Abstract A simple and efficient Bayesian machine learning (BML) training algorithm, which exploits only a 20‐year short observational time series and an approximate prior model, is developed to predict the Niño 3 sea surface temperature (SST) index. The BML forecast significantly outperforms model‐based ensemble predictions and standard machine learning forecasts. Even with a simple feedforward neural network (NN), the BML forecast is skillful for 9.5 months. Remarkably, the BML forecast overcomes the spring predictability barrier to a large extent: the forecast starting from spring remains skillful for nearly 10 months. The BML algorithm can also effectively utilize multiscale features: the BML forecast of SST using SST, thermocline, and windburst improves on the BML forecast using just SST by at least 2 months. Finally, the BML algorithm also reduces the forecast uncertainty of NNs and is robust to input perturbations.