It is well-known that the Hirzebruch–Riemann–Roch theorem in algebraic geometry is a special case of the Atiyah-Singer index theorem. In this talk I will present a proof of the Grothendieck-Riemann-Roch theorem as a special case of the family version of the Atiyah-Singer index theorem. In more details, we first give a Chern-Weil construction of characteristics forms of coherent sheaves in terms of cohesive modules, and then give a heat-kernel proof of Grothendieck-Riemann-Roch theorem. This is a joint work with J.M. Bismut and S. Shen.