The carbon emissions in BRICS countries (Brazil, Russia, India, China and South Africa) account for nearly half of global carbon emissions. To explore the future carbon emissions in BRICS countries and the carbon peak in China and India, the grey Gompertz model with new information priority accumulation is proposed. Intelligent algorithms are used in the parameter optimization. The new model not only increases the influence weight of new information on the predicted results, but also changes the predicted trend of traditional grey prediction model. The effectiveness of the new model for the carbon emission forecast is verified through the known data set. According to the predicted results, the carbon emissions in Russia, Brazil, South Africa tend to stabilize over the long term. The carbon emissions in China and India are rising slowly. China will achieve the carbon peak in 2029 with 10.2 billion tons of carbon emissions. India will not achieve the carbon peak by 2030. The current situations of the carbon emissions in BRICS countries are analyzed. It is concluded that the energy structure, industrial development and the urbanization need to be paid attention to. Detailed policies and suggestions are given in the fourth section. The above research results indicate that the new model can predict the limit value of the carbon emission. The predicted results can provide data support for the policy formulation in carbon reduction.