Use of high-volume fly ash concrete (HVFAC) has to be encouraged in the construction industry for sustainability, by increasing the 28 days’ strength of HVFAC. In India, presently the use of fly ash in concrete is insignificant. The lower consumption may be attributed to the lower quantity of lime in fly ash and the quality of fly ash. Suitably designed HVFAC can solve major problems of concrete construction, if sufficiently early strength can be achieved as required by the construction industry. In the present parametric study, an approach is proposed for achieving comparable 28 days’ strength of HVFAC without fly ash. The proposed concrete used 45% less cement by mass and was cheaper by 20% than control concrete. The results also show that fly ash could increase compressive strength and ultrasonic pulse velocity of concrete by the internal curing effect.