Malaysia is one of the countries that has been experiencing droughts caused by a warming climate. This study considered the Standard Index of Annual Precipitation (SIAP) and Standardized Water Storage Index (SWSI) to represent meteorological and hydrological drought, respectively. The study area is the Langat River Basin, located in the central part of peninsular Malaysia. The analysis was done using rainfall and water level data over 30 years, from 1986 to 2016. Both of the indices were calculated in monthly scale, and two neural network-based models and two wavelet-based artificial neural network (W-ANN) models were developed for monthly droughts. The performance of the SIAP and SWSI models, in terms of the correlation coefficient (R), was 0.899 and 0.968, respectively. The application of a wavelet for preprocessing the raw data in the developed W-ANN models achieved higher correlation coefficients for most of the scenarios. This proves that the created model can predict meteorological and hydrological droughts very close to the observed values. Overall, this study helps us to understand the history of drought conditions over the past 30 years in the Langat River Basin. It further helps us to forecast drought and to assist in water resource management.