This paper proposes a novel nature-inspired meta-heuristic optimizer, called Reptile Search Algorithm (RSA), motivated by the hunting behaviour of Crocodiles. Two main steps of Crocodile behaviour are implemented, such as encircling, which is performed by high walking or belly walking, and hunting, which is performed by hunting coordination or hunting cooperation. The mentioned search methods of the proposed RSA are unique compared to other existing algorithms. The performance of the proposed RSA is evaluated using twenty-three classical test functions, thirty CEC2017 test functions, ten CEC2019 test functions, and seven real-world engineering problems. The obtained results of the proposed RSA are compared to various existing optimization algorithms in the literature. The results of the tested three benchmark functions revealed that the proposed RSA achieved better results than the other competitive optimization algorithms. The results of the Friedman ranking test proved that the RSA is a significantly superior method than other comparative methods. Finally, the results of the examined engineering problems showed that the RSA obtained better results compared to other various methods.