Most El Niño events occur sporadically and peak in a single winter^1–3, whereas La Niña tends to develop after an El Niño and last for two years or longer^4–7. Relative to single-year La Niña, consecutive La Niña features meridionally broader easterly winds and hence a slower heat recharge of the equatorial Pacific^6,7, enabling the cold anomalies to persist, exerting prolonged impacts on global climate, ecosystems and agriculture^8–13. Future changes to multi-year-long La Niña events remain unknown. Here, using climate models under future greenhouse-gas forcings¹⁴, we find an increased frequency of consecutive La Niña ranging from 19 ± 11% in a low-emission scenario to 33 ± 13% in a high-emission scenario, supported by an inter-model consensus stronger in higher-emission scenarios. Under greenhouse warming, a mean-state warming maximum in the subtropical northeastern Pacific enhances the regional thermodynamic response to perturbations, generating anomalous easterlies that are further northward than in the twentieth century in response to El Niño warm anomalies. The sensitivity of the northward-broadened anomaly pattern is further increased by a warming maximum in the equatorial eastern Pacific. The slower heat recharge associated with the northward-broadened easterly anomalies facilitates the cold anomalies of the first-year La Niña to persist into a second-year La Niña. Thus, climate extremes as seen during historical consecutive La Niña episodes probably occur more frequently in the twenty-first century.