Optimal Power Flow (OPF) problem is being solved every day many times in power systems throughout the world by grid operators to get the optimal power dispatch so that the network can be operated reliably and economically. As power system networks evolve through time due to technological growth, and associated increase in demand and Distributed Generations (DG), unpredictability in demand and generation increases. This increase in unpredictability of demand and generation requires the ACOPF (Alternating Current Optimal Power Flow) problem to be solved more frequently in a day than usual, to meet the varying load with minimum cost. Accomplishing this for grid operation using conventional OPF problem solvers is challenging as a decision is required on a fast time scale. The AC-OPF problem can be solved by mathematical solutions; however, they need a significant computation time. Recently to address this challenge machine learning techniques are being investigated. In this thesis, a supervised learning approach to predict solutions for the ACOPF problem by leveraging the general predicting capability of Artificial Neural Networks (ANN) is presented. With exceptional computational performance, artificial neural networks (ANN) are well-suited for function approximation applications. Hence, DNN (Deep Neural Networks) trained from mathematically solved data samples are used to predict ACOPF solutions. To validate the results, the approach is conducted on two standard IEEE test systems: IEEE 14 bus and IEEE 30 bus systems using MATPOWER 7.1 case files on MATLAB R2013a software. Results are compared to the interior point solver, and it is found that feasible solutions are generated with no optimality gap and voltage magnitude deviation of 0.023% from the upper limit at the slack bus with in time scale of 1.62 times faster for the IEEE 14-bus system. For IEEE 30 bus-system solutions are generated in 1.17x faster time scale and average cost deviation of 2.7%. For this system load bus voltage deviations from their upper limits are found to be 0.15% (for 59% of scenarios) at bus 25, and 0.27% deviation (for 8.8% scenarios) at bus 29. Keywords: ANN, DNN, MIPS