Reptile Search Algorithm (RSA) has strong global exploration ability, but its exploitation ability is relatively weak and it cannot converge well in the late stage of the iteration. To address the above issues, combined with the Teaching-Learning-Based Optimization (TLBO) algorithm, the Beetle Antennae Search (BAS) algorithm based on quadratic interpolation and the lens opposite-based learning strategy, Reptile Search Algorithm based on Multi-Hunting Coordination Strategy (MHCS-RSA) was proposed. In MHCS-RSA, the position update formula of the hunting cooperation in the encircling phase (global exploration) and hunting phase (local exploitation) of RSA was retained. And in the hunting coordination of the hunting phase, the learning phase of TLBO algorithm and the BAS based on quadratic interpolation were integrated to perform position update in order to improve the exploitation ability and convergence ability of the algorithm. In addition, the lens opposite-based learning strategy was introduced to enhance the algorithm ability of jumping out of the local optimum. Experimental results on CEC 2020 test functions show that MHCS-RSA has good optimization, convergence abilities and robustness. By solving the tension/compression spring design problem and the speed reducer design problem, the validity of MHCS-RSA is further verified in solving practical problems.