Abstract The magnetic, magnetocaloric and critical behavior properties of 0.8BiFeO3-0.2BaTi0.95(Yb0.5Nb0.5)0.05O3 multiferroic ceramic are studied around its magnetic transition temperature: TC. The Rietveld Refinement of X-ray diffraction data, recorded at room temperature, revealed that our sample crystallizes in the tetragonal P4mm space group. The dependence of magnetization on temperature reveals a magnetic transition at TC = 365 K, which was confirmed via in-situ Mossbauer measurements. Around the magnetic transition temperature TC, the magnetic entropy change reached maximum value of Δ S M M a x of 10.0066 J. kg−1 K−1 and the relative cooling power (RCP) value is of 278.4014 J. kg−1, when a magnetic field of 5T is applied. The critical exponents β, γ and δ have been deduced via various methods: the modified Arrott plots (MAP), Kouvel-Fisher method (KF) and critical isotherm (CI) analysis. These critical exponent values confirm that δ values is between the mean-field model and the 3D-Heisenberg model, the β value is so close to the 3D-Heisenberg model while that γ value is proximate to the mean-field model. These critical parameters associated with the critical magnetic transition region predict the presence of both short and long magnetic range order in our sample. The precision of the deduced critical exponents is highlighted through the follow-up of the dependence of magnetization on temperature and magnetic field to the scaling theory. All the obtained results confirm the coexistence of the effect of two networks in our ceramics, the ferromagnetic ordering spin contribution, resulting in modulating the antiferromagnetic AFM canted spin, and the AFM ones, with both contributions of short- and long-range interactions, respectively, embedded in the spin glass like matrix BiFeO3. A number of attractive features made our 0.8BiFeO3-0.2BaTi0.95(Yb0.5Nb0.5)0.05O3 multiferroics as a potential candidate in a large area of modern applications.