An extraordinary magnetoresistance effect, linearly dependent on the external magnetic field, is observed in amorphous TbFeCo films. The electrical resistance jumps by δρ at magnetization reversal. δρ depends on Tb concentration and it becomes nearly zero at about Tb 26 at. % concentration. To clarify the Tb concentration dependence of δρ, the magnetic properties and the heat treatment effect are examined. It is found that the magnetic anisotropy field (Hk ) is maximum at about Tb 26 at. % and the gradient of linear magnetoresistance, δρ/(ρ0Hc), is proportional to the −Hk+ const, where ρ0 is the electric resistance in zero field, Hc is the coercive force, and the constant is about 100 kOe. The structural relaxation, a coercive force change by the heat treatment up to 200 °C, is examined. It is found that as δρ/(ρ0Hc) in the as-sputtered state decreases, the coercive force change by the heat treatment decreases. The coercive force change is minimum at about Tb 26 at. %, where δρ/(ρ0Hc) becomes zero. These results mean that linear magnetoresistance is related to structure relaxation by heat treatment. The δρ disappearance at about Tb 26 at. % is based on the stable structure against heat treatment and the largest magnetic anisotropy field.