The perovskite TbFe0.5Cr0.5O3 shows two anomalies in the magnetic susceptibility at TN = 257 K and TSR = 190 K which are respectively, the antiferromagnetic and spin reorientation transition that occur in the Fe/Cr sublattice. Analysis of the magnetic susceptibility reveals signatures of Griffiths-like phase in this compound: the negative deviation from ideal Curie-Weiss law and in less-than-unity power-law susceptibility exponents. Neutron diffraction analysis confirms that, as the temperature is reduced from 350 K, a spin reorientation transition from Γ2 (Fx, Cy, Gz) to Γ4 (Gx, Ay, Fz) occurs at TN = 257 K and subsequently, a second spin reorientation takes place from Γ4 (Gx, Ay, Fz) to Γ2 (Fx, Cy, Gz) at TSR = 190 K. The Γ2 (Fx, Cy, Gz) structure is stable until 7.7 K where an ordered moment of 7.74(1)µB/Fe 3+ (Cr 3+ ) is obtained from neutron data refinement. In addition to the long-range order of the magnetic structure, indication of diffuse magnetic scattering at 7.7 K is evident, thereby lending support to the Griffiths-like phase observed in susceptibility. At 7.7 K, Tb develops a ferromagnetic component along the crystallographic a axis. Thermal conductivity, and spin-phonon coupling of TbFe0.5Cr0.5O3 through Raman spectroscopy are studied in the present work. The magnetic anomalies at TN and TSR do not reflect in the thermal conductivity data of TbFe0.5Cr0.5O3; however, it is noticeable that the application of 9 T magnetic field has no effect on the thermal conductivity. The TN and TSR are revealed in the temperature-dependence of full-width-at-half-maximum curves obtained from Raman intensities. An antiferromagnetic structure with (↑↓↑↓) arrangement of Fe/Cr spins is found in the ground state through first-principles energy calculations which supports the experimental magnetic structure at 7.7 K. The spin-resolved total and partial density of states are determined showing that TbFe0.5Cr0.5O3 is insulating with a band gap of ∼ 0.12 (2.4) eV within GGA (GGA+U ) functionals