This study deals with the production of concrete with low CO2 emissions. For this reason, two materials, namely palm oil fuel ash (POFA) and limestone powder (LP), were used as mineral additions to replace conventional cement as much as possible. The results showed that concrete containing 60 wt% POFA could achieve the high strength requirements of ACI 363R from an age of 28 days. At a replacement level of 70 wt% of admixtures, the use of 10 wt% LP + 60 wt% POFA was a good mixture as it had the highest concrete compressive strength, had a minor effect on shrinkage strain and reduced heat generation by approximately 50% compared to cement concrete. Additionally, the use of POFA and LP is a good choice to produce environmentally friendly concrete, which can reduce the CO2 emissions of concrete by about 44–62% compared to cement concrete at similar strength.