Wireless sensor networks (WSNs) are having large demands in enormous applications for the decade. The main issue in WSNs is estimating the exact location of unknown nodes. All applications are dependent on the location information of unknown nodes in WSNs. Location information of mobile anchor node is used to estimate the location of unknown nodes. A new approach is implemented in this paper for the localization of unknown nodes using Artificial Neural Networks. Specifically, a neural feed network is used for the indoor position process. Also several neural network configuration sets have been tested, which includes Bayesian regularisation (BR), Levenberg-Marquardt (LM), resilient back propagation (RP), Scaled Conjugate Gradient (SCG) and Degree Descent (SCG),etc. At the end results are simulated using MATLAB and Mean Square Error is calculated and compared with other existing approaches. The proposed approach is energy efficient and uses only a two-way message to obtain inputs for the localization. Even the cost is minimized as in the proposed system only one mobile anchor node is used.