High-entropy oxides (HEOs) have attracted widespread attention as the next-generation anode materials for lithium-ion batteries (LIBs) due to their low cost and high theoretical capacity. In this work, for the first time, a series of spinel-type cobalt-free (Cr_0.2Fe_0.2Mn_0.2Ni_0.2X_0.2)₃O₄ (X = K, Mg, Zn) high-entropy oxide powders as anode materials for LIBs were synthesized via a solution combustion method. The microstructural features and electrochemical performance of the powders were systematically investigated in comparison with cobalt containing powders of (Cr_0.2Fe_0.2Mn_0.2Ni_0.2Co_0.2)₃O₄. The results indicate that the prepared high-entropy oxide powders are all single-phase of spinel structures, with a porous reticular morphology and uniform distribution of constituent elements. When used as anode materials for LIBs, cobalt-free (Cr_0.2Fe_0.2Mn_0.2Ni_0.2Zn_0.2)₃O₄ exhibits excellent lithium storage performance. After 150 cycles at a current density of 200 mA·g^-1, its reversible specific capacity is up to 1303 mAh·g^-1. Furthermore, after 380 cycles at a high current density of 1000 mA·g^-1, the reversible capacity can still reach 1190 mAh·g^-1 (both are higher than its theoretical capacity of 908 mAh·g^-1). The reasons for the excellent lithium storage performance of 4MZn electrode are: high specific surface area, mesoporous structure, and abundant oxygen vacancies on the surface make it a high conductivity (12.2 S·m^-1) and a large pseudo-capacitance contribution rate; At the same time, the addition of active element Zn causes the formation of Li-Zn alloy in the reduction process of 4MZn electrode, thereby increasing its specific capacity. This work provides a new design approach for exploring cobalt free high entropy energy storage materials with low cost and excellent electrochemical performance.