Correct inference of genetic regulations inside a cell from the biological database like time series microarray data is one of the greatest challenges in post genomic era for biologists and researchers. Recurrent Neural Network (RNN) is one of the most popular and simple approach to model the dynamics as well as to infer correct dependencies among genes. Inspired by the behavior of social elephants, we propose a new metaheuristic namely Elephant Swarm Water Search Algorithm (ESWSA) to infer Gene Regulatory Network (GRN). This algorithm is mainly based on the water search strategy of intelligent and social elephants during drought, utilizing the different types of communication techniques. Initially, the algorithm is tested against benchmark small and medium scale artificial genetic networks without and with presence of different noise levels and the efficiency was observed in term of parametric error, minimum fitness value, execution time, accuracy of prediction of true regulation, etc. Next, the proposed algorithm is tested against the real time gene expression data of Escherichia Coli SOS Network and results were also compared with others state of the art optimization methods. The experimental results suggest that ESWSA is very efficient for GRN inference problem and performs better than other methods in many ways.