In this work, the structural properties, stability, electrical properties, elasticity, and magnetic properties of the rare earth and intermetallic compound DyFe2, Dy4Co4Fe16, and Dy8Fe12Co4 systems were investigated by first principle calculations. At the same time, the GGA+U method is used to correct for the self-interaction errors (SIE) encountered in the calculations. Specifically, the first nature principle is used to calculate the formation energy as well as the elastic matrix, and the results show that those systems are thermodynamically stable as well as mechanically stable. Co doping at different positions causes more changes for the electrical properties leading to asymmetric enhancement of spin-up and spin-down energy bands, and Dy-f electron orbitals become active, and orbital hybridization occurs between Dy-f and Co-d in the Dy8Fe12Co4 system. For the elastic property analysis, it was found that all three systems were ductile, but the Young’s modulus of Dy4Co4Fe16 varied the most compared to the intrinsic DyFe2. The magnetic change is most obvious after the Co were doped in the intrinsic DyFe2, which makes a part of the Fe atoms unevenly distributed magnetic moments.