BaTiO3 based ceramics were prepared by solid state reaction. Mn and Nb were co-doped in the B site of BaTiO3 based ceramics. The effect of donor and acceptor (Nb and Mn) on the dielectric properties of BaTiO3 based ceramics was investigated. The Mn = 1.6% mol and Nb = 0, 0.18%, 1.0%, 1.1%, and 2.0% mol respectively. When the content of Nb is less than 1.0% mol (Mn is fixed at 1.6% mol), the temperature dependence of the dielectric constant appeared a diffuse phase transition(DFT) characteristics, and a normal-like ferroelectric characteristics was observed as the content of Nb is 1.0% mol. When the content of Nb increases further, up to 1.1% mol, it showed a dielectric relaxation. Atomic computer simulation has been used to predict the binding energy for different defect associations [2NbTi.+VBa''] and [2VO..+MnTi''] which leads to random electrical fields and polar nanoregions (PNRs). The change from DFT ferroelectrics to relaxors could be related to the size of PNRs.