Replacing cement with lithium slag and fine aggregate with rubber in concrete solves waste disposal, reduces material consumption, boosts sustainability, and enhances concrete performance. A set of prismatic concrete specimens with varying proportions were designed and experimentally tested in order to study the compressive stress-strain behavior of lithium slag rubber concrete (LSRC). The main factors affecting the specimens were lithium slag substitution ratio (SL=0%, 10%, 20%, 30%) and rubber substitution ratio (SR=0%, 5%, 10%, 15%). The results demonstrated that the LSRC exhibited good integrity during the damage. Furthermore, the incorporation of lithium slag (LS) was found to effectively compensate for the reduction in compressive strength due to the incorporation of rubber. When 10% of the fine aggregate was replaced with rubber and 20% of the cement was substituted with lithium slag, the axial compressive strength, elastic modulus, and peak strain of the tested specimens increased by 21.57%, 6.92%, and 17.26%, respectively. Compared with ordinary concrete, LSRC has good toughness, impact resistance and durability with minimal loss of strength, and has broad application prospects in engineering fields (such as airports, highways, housing expansion joints, concrete floors and railway concrete sleepers, etc.). Based on the experimental data, simplified modified equations to predict the compressive strength, elastic modulus, peak strain and axial stress-strain constitutive model of LSRC were proposed, so as to promote the development of LSRC.