A high early strength pozzolan cement includes larger sized pozzolan particles blended with smaller sized hydraulic cement particles containing tricalcium silicate and/or dicalcium silicate (e.g., Portland cement). Excess calcium release from the hydraulic cement when mixed with water forms calcium hydroxide available for reaction with the pozzolan. The fineness of the hydraulic cement particles is substantially greater than the fineness of the pozzolan particles (e.g., about 1.25 to about 50 times greater). Reducing or eliminating coarse hydraulic cement particles that cannot fully hydrate but include unreacted cores reduces or eliminates wasted cement normally found in concrete. Replacing some or all of the coarse cement particles with pozzolan particles provides a pozzolan cement composition having significantly lower water demand compared to the hydraulic cement by itself.