The superconducting pyrochlore oxide Cd2Re2O7 shows a structural transition with inversion symmetry breaking (ISB) at Ts1 = 200 K. A recent theory [L. Fu, Phys. Rev. Lett. 115, 026401 (2015)] suggests that the origin is an electronic instability that leads to a multipolar order in the spin-orbit-coupled metal. To observe the Fermi surface of the low-temperature phase of Cd2Re2O7, we perform de Haas-van Alphen effect measurements by means of magnetic torque. In reference to a calculated band structure, the spin-split Fermi surfaces with large cyclotron masses of 5-9m0 are revealed. The splitting is suggested to be due to an antisymmetric spin-orbit coupling induced by ISB, the strength of which is estimated to be approximately 67 K, which is rather smaller than those of typical non-centrosymmetric metals.