A kind of stabilized time discontinuous space-time finite element formulations are presented for the convection-reaction-diffusion equations. The stabilized schemes considered in this paper are constructed based on the streamline upwind Petrov-Galerkin (SUPG) finite element approximate scheme, combining with the space time finite element method in which the discrete time variation form was used. The theoretical proofs of the scheme cannot be found in relative references, although there are some simulations in practical applications. In this paper, we give the proofs of stability and error estimates in the maximum norm of time and L²(Ω)-norm of spatial by taking the Radau points as the interpolation nodes of Lagrange interpolation polynomials. The temporal and spacial variants are decoupled, the restricted conditions on the space-time meshes are removed by taking advantages of the techniques of combining the interpolation polynomials with the finite element method. The process of of proof in this paper provides a new idea of theoretical analysis for the stabilized space time finite element method permitting discontinuities in time. And the complexities in practical computations caused by the unifying space and time variables are conquered.