Calculation of 6R serial manipulator's inverse kinematics is a highly complex nonlinear mapping problem. As the process of 6R serial manipulator's inverse kinematics calculating concerned, these traditional algorithms, like inverse transformation, geometry, pieper solution, etc., are very complex, and they often involve in the problem of multiple solutions and singularity. So, the calculation efficiency is very low. Artificial Neural Network (ANN) has a great advantage in solving these problems of nonlinear mapping, like parallel processing, self-adaptive, and fast, efficient handling of the multivariable system, etc. So, ANN has been widely used to solve the complex kinematics problems of the redundant robotic manipulators. This paper adopts a RBF-based neural network to solve the inverse kinematics problem of 6R serial manipulator. From the final simulation, we can find that, by using this new calculating algorithm, it can give an accurate inverse kinematics solution fast and with a high efficiency. Apart from these, when using in practice, it also reflects a perfect performance.