Modelling of plates with internal defects or cut outs is often an issue in the traditional isogeometric methods and hence extended isogeometric methods are developed. In order to reduce the computational cost involved in extended isogeometric methods based on weak form, a new extended isogeometric hybrid collocation–Galerkin method is proposed in the present paper. The natural frequencies of a homogeneous and functionally graded material plate with internal defects of varying gradient index, sizes and shapes are obtained using the proposed method. The obtained results are compared and found to be in good agreement with the reference results. © 2018, © 2018 Taylor & Francis Group, LLC.