We have demonstrated magnetodielectric (MD) coupling in an Ising-chain magnet Sr2Ca2CoMn2O9 via detailed investigation of ac susceptibility and dielectric constant as a function of temperature, magnetic field, and frequency. Sr2Ca2CoMn2O9 consists of spin-chains made of the regular stacking of one CoO6 trigonal prism with two MnO6 octahedra. The (Co2+-Mn4+-Mn4+) unit stabilizes a (↑↓↑) spin-state along the chains that are distributed on a triangular lattice. This compound undergoes a partially disordered antiferromagnetic transition at TN ∼ 28 K. The dielectric constant exhibits a clear peak at TN only in the presence of an external magnetic field (H ≥ 5 kOe), evidencing the presence of MD coupling, which is further confirmed by field-dependent dielectric measurements. We argue that spatial inversion symmetry can be broken as a result of exchangestriction along each spin chain, inducing uncompensated local dipoles. At low temperatures, a dipolar relaxation phenomenon is observed, bearing strong similarities to the blocking effect typical of spin dynamics in this compound. Such a spin-dipole relationship is referred to as a "multiblocking" effect, in relation to the concept of magnetodielectric "multiglass" previously introduced for related materials.