In petroleum production system, interwell connectivity evaluation is a significant process to understand reservoir properties comprehensively, determine water injection rate scientifically, and enhance oil recovery effectively for oil and gas field. In this paper, a novel long short-term memory (LSTM) neural network based global sensitivity analysis (GSA) method is proposed to analyse injector-producer relationship. LSTM neural network is employed to build up the mapping relationship between production wells and surrounding injection wells using the massive historical injection and production fluctuation data of a synthetic reservoir model. Next, the extended Fourier amplitude sensitivity test (EFAST) based GSA approach is utilized to evaluate interwell connectivity on the basis of the generated LSTM model. Finally, the presented LSTM based EFAST sensitivity analysis method is applied to a benchmark test and a synthetic reservoir model. Experimental results show that the proposed technique is an efficient method for estimating interwell connectivity.