In our article, inverse kinematic problem of a plasma cutting robot with three degree of freedom is solved using artificial neural networks. Artificial neural network was trained using joint angle values according to cartesian coordinates (x, y, z) of end point of a robotic arm. The Levenberg-Marquardt training algorithm was applied to educate artificial neural network. To validate the designed neural network, it was tested using a new test data set which is not applied in training. A simulation was performed on a three-dimensional model of MSC.ADAMS software using angle values obtained from artificial neural network test. It was revealed from this simulation that trajectory of plasma cutting torch obtained using artificial neural network agreed well with desired trajectory.