Many eukaryotic photosynthetic organisms enhance their carbon uptake by supplying concentrated CO to the CO-fixing enzyme Rubisco in an organelle called the pyrenoid. Ongoing efforts seek to engineer this pyrenoid-based CO-concentrating mechanism (PCCM) into crops to increase yields. Here we develop a computational model for a PCCM on the basis of the postulated mechanism in the green alga Chlamydomonas reinhardtii. Our model recapitulates all Chlamydomonas PCCM-deficient mutant phenotypes and yields general biophysical principles underlying the PCCM. We show that an effective and energetically efficient PCCM requires a physical barrier to reduce pyrenoid CO leakage, as well as proper enzyme localization to reduce futile cycling between CO and HCO. Importantly, our model demonstrates the feasibility of a purely passive CO uptake strategy at air-level CO, while active HCO uptake proves advantageous at lower CO levels. We propose a four-step engineering path to increase the rate of CO fixation in the plant chloroplast up to threefold at a theoretical cost of only 1.3 ATP per CO fixed, thereby offering a framework to guide the engineering of a PCCM into land plants.