An immersed virtual element method is developed to solve the second-order interface problems in two-dimensional space

which overcomes the problem that the constructed space cannot satisfy both the coordination and jump conditions. The key idea is to use the conforming virtual element spaces on a shape regular background unfitted mesh for discretization

and project them to the immersed finite element spaces on interface elements which are cut by the interfaces from the background mesh

making the proposed method combine the advantages of both body-fitted mesh methods and unfitted mesh methods. Then the strict theoretical derivation and optimal error estimation of the method are given. Finally

the numerical example is solved. By calculating the L2 and H1 norms of the numerical solution and analytical solution

and making the linear regression diagram of errors

the method achieves second order convergence in the L2 norm and first order convergence in the H1 norm

indicating that the theoretical analysis results are correct.