High-entropy oxides (HEOs) have become increasingly popular as energy storage materials owing to their unique high-entropy effect, multi-principal synergy effect and customizable structure. In this study, a series of cobalt-free perovskite high-entropy oxide La(Cr_0.2Fe_0.2Mn_0.2Ni_0.2M_0.2)O₃ (M=Cu, Mg, Zn) lithium-ion battery anode materials were successfully synthesized by solution combustion method using metal nitrate as the metal source and glycine as the fuel. The microstructure and electrochemical properties of the as-prepared powders were investigated. The results show that the as-prepared high- entropy oxides crystalize into single-phase perovskite structure with porous foam-like shape and chemical/microstructural homogeneity. Furthermore, the as-prepared HEOs introducing inactive element Mg or active element Cu possess similar electrochemical performance; while the La(Cr_0.2Fe_0.2Mn_0.2Ni_0.2Zn_0.2)O₃ electrode exhibits a highest reversible capacity (1014 mAh•g⁻¹ at 200 mA•g⁻¹ after 250 cycles), excellent cycling stability (450 mAh•g⁻¹ at 1000 mA•g⁻¹ and almost no capacity decay after 1000 cycles) and outstanding rate performance. Such excellent performance can be attributed to the addition of active element Zn, which can form Li-Zn alloy during the reduction process that makes the specific capacity increase significantly. Meanwhile, its higher specific surface area, mesoporous structure and abundant surface oxygen vacancies result in higher conductivity (0.14 S•cm⁻¹), increased larger lithium ion diffusion coefficient (2.1×10⁻¹² cm²•s⁻¹), and pseudo-capacitance contribution, thus significantly enhances the specific capacity and rate performance of the as-prepared material. Therefore, the introduction of electrochemically active metals, which can react with Li alloying, such as Zn, can improve the electrochemical performance, thereby providing ideas for designing cobalt-free HEOs with low-cost and excellent performance for energy storage.