The most important duty of a distillation column is separation and production of products with certain purity. In this project a model for a distillation tower including 7 equilibrium stages for separation of a methanol-water mixture for study on production purity control was developed. After modeling, simulation of the distillation tower was carried out and the results are compared with experimental data in order to evaluate the accuracy of modeling and simulation. In various applications, conventional controllers such as Proportional Integral Derivative (PID) were used widely with reasonable operation. But in processes with long delay, complex, and non-linear have not suitable performance. Neural Networks with their high learning ability and estimation of non-linear functions with high accuracy are a new method in modeling, simulation and control of process. Thus, neural network model are used for simulation and control of distillation column. Also, effects of various parameters, such as number of neurons in hidden layer, training algorithms, training speed parameter, number of learning data in neural network, and span of input data were studied. Matrix of relative gains for distillation column was developed and based on it; couples of suitable input-output variables were selected. Temperature of bottom product with reboiler thermal flux, and temperature of top product with reflux ratio were selected as two control loops. In this project for identification and control of distillation column purity, neural network controllers were design. Levenberg-Marquardt algorithm was the best method in training of distillation column neural network. The neural network controller in comparison with the PID controller had lower offset, overshoot, and response time.