This thesis describes a new approach for achieving a non-planar 3D printing with an industrial manipulator. In recent years 3D printing is becoming a promising new industry. It is applied in more and more areas. Simultaneously, with the improvement of production efficiency, the cost for industrial robots is decreasing. Our motivation is to combine the two technologies and to develop a method using a robot to expand the practical range of 3D printing. In this work firstly the basic concepts about robot kinematic modelling are introduced. Then the essential hard- and software equipment that is chosen to solve the problem is described. A method is presented using a laser distance sensor mounted on a robot to scan an arbitrary surface. Levenberg-Marquardt method is applied to find a least-mean-square approximation and to reconstruct the non-planar surface in real-time during the motion of the robot, which carries also a 3D printer head. For testing the algorithms a virtual reality simulation model of the robot was used. Finally the solution is successfully implemented in a Matlab/Simulink environment that controls the robot drives in real-time. With this work the feasibility of a non-planar 3D printing with an industrial robot is proved. A practicable approach consisting of surface scanning and printing is successfully applied on a real robot. At last some tracking error considerations are given.