This study presents implementation of non-linear autoregressive model with exogenous inputs (NARX) of Artificial neural network (ANN), used for groundwater level (GWL) simulation to predict its weekly level up to 52 weeks ahead in selected 14 Permanent Hydrograph Stations (PHSs) in the drought prone Barind Tract in the northwestern part of Bangladesh and is considered to be the first attempt of this type in the country. In this regard, the weekly historical time series climatological data (rainfall, temperature, humidity and evaporation) during 1980–2017 have been used as input variables to forecast GWL. Auto-correlation of GWL time series data to find out the dependent relationship between current GWL to the previous level were carried out and cross-correlation between GWL and rainfall have been used to find out the effectiveness with time. Here GWL is mostly influenced by rainfall having lagged continuation with corresponding peak (max) and trough (min) of rainfall indicating time delayed response of 11.25–14.0 (avg. 12.73) weeks. Analysis before training of ANN reveals that NARX models are good in prediction. Moreover, rainfall has affected by climatological parameters where rainfall is one of the potential input parameter influencing GWL. In recent years, groundwater withdrawals are higher than the rainwater recharge to aquifer due to continuous expansion of irrigated agriculture in the area. Finally, present study as pioneer approach provides significant contributions for groundwater management in resource planning of Bangladesh.