The number of older adults with Alzheimer's disease is increasing every year. The associated memory problems cause many difficulties for Alzheimer's patients and their caretakers; patients may even become lost in familiar surroundings. In this paper, a proposed localization system based on a wireless sensor network (WSN) and backpropagation based artificial neural network (BP-ANN) was practically implemented to detect and determine the position of an Alzheimer's patient in an indoor environment. The proposed system consisted of four ZigBee-based XBee S2C anchor nodes and one mobile node carried by the Alzheimer's patient. The received signal strength indicator (RSSI) of the anchor nodes was collected by the mobile node using a laptop supported by X-CTU software. The obtained RSSI values were used as input for training, testing, and validation processes of the BP-ANN, while two-dimension (2D) locations (x and y) were used as the output of the ANN. The results showed that the obtained mean localization errors were 0.964 and 0.921m for validation and testing phases, respectively, after applying the ANN. Based on a comparison with state-ofthe-art technology, we deduced that the proposed ANN method outperformed other techniques in previous studies in terms of mean localization error.