Our polycrystalline sample study on the Yb-based chalcogenide spinels AYb(2)X(4)(A = Cd, Mg; X = S, Se) has revealed frustrated magnetism due to the antiferromagnetically coupled Heisenberg spin on a pyrochlore lattice. The crystal electric field analysis indicates the Yb ground state has nearly Heisenberg spins with a strong quantum character of the ground doublet. All the materials exhibit an antiferromagnetic order at 1.4-1.8 K, much lower temperatures than the antiferromagnetic exchange coupling scale of similar to 10 K. The magnetic specific heat CM shows a T-3 dependence, indicating the gapless feature in the Yb-based chalcogenide spinels. The magnetic entropy change much smaller than R ln 2 below the Neel temperature and the small local magnetic field estimated from the mu SR measurements strongly suggest the significantly reduced size of the ordered moment in comparison with the bare moment size 1.33 mu(B)/Yb, supporting strong fluctuations in the commensurate and incommensurate ordered states in CdYb2S4 and MgYb2S4, respectively.