In this paper, we intend to formulate a new Cuckoo Search (NCS) for solving optimization problems. This algorithm is based on the obligate brood parasitic behavior of some cuckoo species in combination with the Lévy flight behavior of some birds and fruit flies, at the same time, combine particle swarm optimization (PSO), evolutionary computation technique. It is tested with a set of benchmark continuous functions and compared their optimization results, and we validate the proposed NCS against test functions with big size and then compare its performance with those of PSO and original Cuckoo search. Finally, we discuss the implication of the results and suggestion for further research.