Abstract: NURBS-based isogeometric analysis method provides an effective integration between the CAGD and the finite element analysis.In this paper,the isogeometric analysis method is applied to two-dimensional linear convection-diffusion problems.First,a new stable and discrete solution is proposed by combining the SUPG(streamline upwind Petrov-Galerkin) method and the isogeometric analysis method,and thus,the discrete stable format of isogeometric solution is established.Then time domain is discretized by the θ weighting method to get the final isogeometric solution form which is fully discrete.At the same time,to reduce the essential boundary handling error caused by non-interpolation of NURBS basis function,the penalty function is introduced.Finally,two numerical examples are presented to prove the effectiveness of the approach.