Three new Anderson-type polyoxometalate (POM)-based metal–organic frameworks (POMOFs) [Co3(L1)(TeMo6O24)(H2O)10]·8H2O (1), [Co3(L2)(TeMo6O24)(H2O)10]·8H2O (2) and [Cu3(L1)(TeMo6O24)(H2O)10]·6H2O (3) (L1 = N,N′-bis(4-pyrimidinecarboxamido)-1,2-ethane, L2 = N,N′-bis(4-pyrimidinecarboxamido)-1,4-butane) were obtained under 90 °C aqueous solution for two days. POMOFs 1–3 show fascinating 3D framework structures formed by transition metal linking bis(pyrimidine)-bis(amide) ligands and Anderson-type [TeMo6O24]6– anions. The carbon paste electrodes bulk-modified by POMOFs 1–3 (1-, 2-, 3-CPEs) have good bifunctional electrocatalytic performance towards the oxidation of ascorbic acid and the reduction of potassium bromate, potassium nitrite and heavy metal ions Cr(VI). 1-, 2-, 3-CPEs can be used as electrochemical sensors for the detection of Cr(VI), the limits of detection (LODs) are 0.389 ∼ 0.422 μM, which are lower than the 1.0 μM standard set by the WHO. In addition, the adsorption properties of POMOFs 1–3 on organic dyes gentian violet (GV) and methyl orange (MO) were investigated.