A cement clinker which necessitates no considerable change in the main chemical components and mineral components of cement, is free from preheater coating problems and adverse influences on cement properties, and is effective in reducing the heat quantity required for burning; and a process for producing the cement clinker. In the process for cement clinker production a substance having a melting point higher than the temperature of a liquid phase of the cement clinker and serving as crystal nuclei for C3S is incorporated include a fine powder of refractory brick, particles of an ordinary Portland cement clinker, a fine powder of a high-early-strength Portland cement clinker, a high-early-strength Portland cement, and a fine powder of quicklime. Due to this, alite generation is accelerated even at a low temperature. As a result, high-quality clinker can be produced through burning using a small unit heat quantity and no decrease in cement quality results. The process contributes to a reduction in preheater coating amount and prolongation of the life of the refractory bricks.