Compounds with composition Tb2Fe29-xCrx (x=1.0, 1.5, 2.0, and 3.0) have been synthesized successfully. The lattice parameters, the unit cell volume, the density, and the atomic positions of these compounds have been derived from x-ray diffraction patterns. The Curie temperature, the saturation magnetization, and the anisotropy field at 4.2 K and room temperature bf these compounds are also obtained. The saturation magnetization of Tb3Fe29-xCx decreases but the anisotropy field increases Linearly with increasing Cr concentration at 4.2 K and room temperature. A spin reorientation of the easy-magnetization direction occurs at around 180 K and a first-order magnetization process is observed in magnetic fields in the range between 2.3 and 1.6 T at room temperature for the Tb3Fe29-xCrx compounds. The relationship between the hexagonal R2T17 (2:17H), tetragonal RT12-xTx' (1:12), and monoclinic R3T29-xTx' (3:29) structures are obtained through the matrix transformation of reciprocal vectors in a Cartesian coordinate system. Based on the experimental results of the saturation magnetization and the average hyperfine field of TD3Fe29-xCrx compounds, the, average Fe atomic magnetic moments in the range 0 less than or equal to x less than or equal to 3 can be expressed as an empirical formula: M-Fe=M-Fe(1) -x[M-Fe(1)-M-Fe(2)]/X-max where M-Fe(1) is the iron moment in 2:17 compounds, M-Fe(2) is the iron moment in 1:12 compounds and X-max=3 is the highest Cr concentration included.