The perovskite TbFe 0.5 Cr 0.5 O 3 shows two anomalies in its magnetic susceptibility at T N = 257 K and T SR = 190 K which are, respectively, the antiferromagnetic and spin-reorientation transition that occur in the Fe/Cr sublattice. Magnetic susceptibility of this compound reveals canonical signatures of a Griffiths-like phase: a negative deviation from the ideal Curie-Weiss law and in less-than-unity power-law susceptibility exponents. Neutron-diffraction data analysis confirms two spin-reorientation transitions in this compound. The first one from 2 (C x , G y , F z ) to 4 (A x , F y , G z ) occurs at T N = 257 K and a second one from 4 (A x , F y , G z ) to 2 (C x , G y , F z ) at T SR = 190 K in the Pnma space-group setting. The 2 (C x , G y , F z ) structure is stable down to 7.7 K, leading to an ordered moment of 3.34(1) μ B /Fe 3+ (Cr 3+ ). In addition to the long-range magnetic order, experimental indication of diffuse magnetism is observed in neutron-diffraction data at 7.7 K. Tb develops a ferromagnetic component along the z axis at 20 K. Thermal conductivity and spin-phonon coupling of TbFe 0.5 Cr 0.5 O 3 studied through Raman spectroscopy are also presented in the paper. The magnetic anomalies at T N and T SR do not appear in the thermal conductivity of TbFe 0.5 Cr 0.5 O 3 , which appears to be robust up to 9 T. On the other hand, they are revealed in the temperature dependence of full-width-at-half-maximum curves derived from Raman intensities. An antiferromagnetic structure with ↑↓↑↓ arrangement of Fe/Cr spins is found as the ground state through first-principles energy calculations, supporting the experimentally determined magnetic structure at 7.7 K. The spin-resolved total and partial density of states show that TbFe 0.5 Cr 0.5 O 3 is insulating with a band gap of ∼0.12 (2.4) eV within GGA (GGA+U ) functionals.