A novel Tb3(Fe,Cr)29 single crystal, which has a monoclinic Nd3(Fe,Ti)29-type structure, is obtained using the Czochralski method by performing a proper heat treatment on the Tb2Fe16.46Cr1.23 crystal with a Th2Ni17-type structure. Thermomagnetic curves along the easy axis and magnetization curves along the easy and hard axes are presented for both crystals. The lattice parameters are a = 1.058 nm, b = 0.848 nm, c = 0.968 nm, α = γ = 90°, and β = 96.93° for the Tb3(Fe,Cr)29 single crystal. The Curie temperatures, saturation magnetizations, and magnetocrystalline anisotropy constants are compared between the Tb-2:17 and Tb-3:29 crystals. The magnetization behavior along the hard axis is quite different as a first-order magnetization process (FOMP) of type I for the Tb-2:17, but a FOMP of type II for the Tb-3:29 crystal is observed below room temperature. At low temperatures, magnetohistory effects are detected for both crystals.