In complex network analysis, identifying the viral nodes is a major concern of the research domain by which any kind of information or infection is controlled throughout the entire network. Several algorithms have been developed over the past few years to identify the viral nodes (influential spreaders) considering many properties of the network. Among them, some authors proposed gravity-based centrality to identify the vital nodes based on the law of gravity with certain limitations. The major limitation of existing gravity-based methods is the mass of the object (i.e. node) is considered as the degree or kshell index only, which does not always signify the spreading ability of the nodes. To address this research challenge, we propose an innovative Local Closeness Gravity method (named LCG) to measure the influential ability of individual nodes, facilitating the identification of the vital nodes in the network. To minimize the computational complexity of Closeness centrality, at first, we measure the local Closeness centrality of individual nodes considering all the nodes residing in the truncation radius. Thereafter we introduce a new parameter “information sharing ability” based on connectivity strength to measure the distance between the nodes. Finally, the influential ability of each node is measured based on the gravity model considering the local closeness centrality, kshell index, and the distance. The efficiency of LCG is compared with the existing baseline centrality methods by using the Susceptible-Infectious-Recovered (SIR) simulator. The correlation between the LCG method and the baseline centrality methods with the SIR method is compared by Kendalls' tau method considering various infection probabilities and various percentages of seed nodes respectively. The ranking uniqueness of the LCG method and the baseline centrality methods are also measured by the monotonicity metrics. Through the obtained results and various analyses, it becomes evident that the LCG method adeptly discerns the vital nodes within the networks.