The main objective of this research work was to use Artificial Neural Network (ANN) based method for solving Power Flow Problem for a power system in Nigeria. This was achieved using the Backpropagation (multilayered feed-forward) Neural Network model. Two Backpropagation neural networks were designed and trained; one for computing voltage magnitudes on all buses and the other for computing voltage phase angles on all PV and PQ buses for different load and generation conditions for a 7-bus 132 kV power system in South-West Nigeria (Ayede). Due to unavailability of historical field records, data representing different scenarios of loading and/or generation conditions had to be generated using Newton-Raphson non-linear iterative method. A total of 250 scenarios were generated out of which 50% were used to train the ANNs, 25% were used for validation and the remaining 25% were used as test data for the ANNs. The test data results showed very high accuracy for the ANN used for computing voltage magnitudes for all test data with a Mean Square Error (MSE) of less than 10-6. Also, the ANN used for computing voltage phase angles showed very high accuracy in about 80% of the test data and acceptable results in about 97% of the test data. The MSE for all the test data results for the ANN computing voltage phase angles was less than 10-2.