The Haldane spin-chain compound, Tb2BaNiO5, has been known to order antiferromagnetically below (TN=) 63 K. The present magnetic studies on the polycrystals bring out that there is another magnetic transition at a lower temperature (T2=) 25 K, with a pronounced magnetic-field induced metamagnetic and metaelectric behavior. Multiferroic features are found below T2 only, and not at TN. The most intriguing observation is that the observed change of dielectric constant (Δε) is intrinsic and largest (e.g., ~ 18% at 15 K) within this Haldane spin-chain family, R2BaNiO5. Taking into account the fact that this trend (that is, the largest value of Δε for Tb case within this family) correlates well with a similar trend in TN (with the values of TN being ~55, 58, 53 and 32 K for Gd, Dy, Ho and Er cases), we believe that the explanation usually offered for this TN behavior in rare-earth systems is applicable for this Δε behavior as well. That is, single-ion anisotropy following crystal-field splitting is responsible for the extraordinary magnetodielectric effect in this Tb case. To our knowledge, such an observation was not made in the past literature of multiferroics.