  The interior penalty methods using $C^0$ Lagrange elements ($C^0$IPG)
developed in the last decade for the fourth order problems are an interesting
topic in academia at present. In this paper, we discuss the adaptive fashion of
$C^0$IPG method for the Helmholtz transmission eigenvalue problem.We give the a
posteriori error indicators for primal and dual eigenfunctions, and prove their
reliability and efficiency. We also give the a posteriori error indicator for
eigenvalues and design a $C^0$IPG adaptive algorithm. Numerical experiments
show that this algorithm is efficient and can get the optimal convergence rate.
