Abstarct: Plate structures are one of the most important structural systems that are used in many engineering works and modern industries; Therefore, optimizing them is important. Topology optimization is one of the fields of structural optimization that has recently been considered by many researchers and its purpose is to find the best distribution of materials in the design domain by considering the objective function and specific constraints This study presents topology optimization of plate structures by employing isogeometrical level set method. For structural analysis of plates, the IsoGeometric Analysis (IGA) approach is applied and Non-Uniform Rational B-Splines (NURBS) basis functions are used for approximation of the design domain geometry as well as the unknown deformation field. In previous studies, the level set function has been approximated using the b-spline basis functions, and the control net is updated during the optimization process. Since the control points are not basically on the level set surfaces, the difference between the zero level of the level set function, which shows the boundaries of the structure, and the zero level of its control net appears. to alleviate this difference and increase the accuracy, in this study the level set function is parametrized with Radial Basis Functions (RBFs) over a grid defined in parameter space which is constantly a unite square for each patch of the model. Therefore, the control net in the isogeometric analysis model and the grid for solve the level set function are separate. therefore, for problems with complicated design domains the level set function can be solved in a uniform grid. the level set function is solved in parameter space and the updated level set function is mapped into physical space. This approach can handle the problems with complicated design domains and with an approximate re-initialization scheme can maintain a smooth level set function during the optimization process and has less dependency on initial designs because of its ability to nucleate new holes inside the design domain. Due to the capability of IGA method in modeling complex design domains, while maintaining high accuracy in analysis, combination of IGA with RBFs level set method provides a very useful and effective technique for topology optimization problems. in this study, like most common topology optimization problems, compliance is minimized by considering the volume constraint of the material. Several numerical examples are prepared to demonstrate the efficiency and accuracy of the method for topology optimization of the plate structures and to evaluate the validity of the method, the obtained optimal topologies are compared with the optimal topology presented for plate structures with other methods in the existing literature.