A calcium sulfoaluminate-based concrete with a permeability of less than 1000 Coulombs. Rapid-setting low chloride-ion permeability calcium sulfoaluminate (CSA) cements and concretes include CSA and a suitable polymer such as a sol-gel derived, organic-inorganic, silica based hybrid coating solutions of polystyrene-butylacrylate polymers containing active silanol groups protected by hydroxyl groups containing polyalcohol, or other polymers. Such polymers may be added as powders or as liquid in the finish mill. Other rapid-setting low chloride-ion permeability (CSA) cements and concretes include CSA with selected particle size distributions, and do not require use of any polymer. These CSA cements and concretes have low chloride-ion permeability, high early strength, fast setting times, low-shrinkage, and high freeze-thaw resistance.