With the rapid progress in smart grid, data required to be processed by the state estimation algorithm increases sharply. However, the existing serial algorithms suffered from lower computing speed and cannot meet the requirement of real-time analysis; while deployment of the parallel algorithms needs large scale computing cluster which occupies huge amount of hardware resources and resulting in high energy cost. To overcome above mentioned problems, this paper proposes a Neural Network (NN) based state estimation algorithm. The proposed algorithm constructs and trains the neural network in an offline manner. While solving the actual estimation problem, the iterative least square fitting in traditional state estimation schemes is replaced with forward calculation of the trained neural network. This can reduce execution time of the overall state estimation algorithm significantly. Because the time consumed by forward calculation of the neural networks is very short, the proposed algorithm can still run on a single machine even confronting with large scale power grid, so as to avoid the energy consumption required for computing cluster. Moreover, the neural network has high robustness and can effectively correct the gross error in the measured data. The performance comparison demonstrates that the calculation speed of the proposed scheme is improved by 205 times compared with the serial algorithm. This work is supported by Natural Science Foundation of Hebei Province (No. F2017502043).