The authors studied the relationship between the strength development and hydration reaction in concrete containing silica fume and having an actual strength of 150 MPa or more. By the age of 91 days, concrete that had been exposed to a high-temperature history at an early age by a simple adiabatic curing method was 20 to 30 MPa stronger than concrete that had been cured by the standard method. This result was opposite to the tendency, well-known in Japan conventionally, of concrete without silica fume and having a compressive strength in the range of 60 to 80 MPa. The water content required for hydration was so small that it took one year or more by the standard curing method to develop the potential strength such a low water-binder ratio. On the other hand, we clarified that when structural concrete is exposed to a high-temperature history at an early age, the reaction of the silica fume increases remarkably, to obtain the strength near to the potential at an early age, thereby further widening the difference in strength between this concrete and concrete cured by the standard method. The reaction rate of cement-silica fume binder cured by the simple adiabatic method for 7 days was higher than in that cured by the standard method for 1 year, which corresponds to the trend in strength development.