The effects of dynamics of entangled two-mode Gaussian coupled states in contact with a thermal reservoir on fidelity of teleportation are investigated. We study and compare entangled squeezed vacuum states with entangled squeezed thermal states as initial resource for quantum teleportation in the system composed of two coupled bosonic modes in contact with a thermal bath studied in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. The evolution of the system is described in terms of covariance matrices. We show that fidelity of teleportation decreases with the increase of number of thermal photons, therefore the squeezed vacuum state is the best resource for quantum teleportation. Moreover, we find the optimal values of squeezing and coupling parameters to obtain maximal values of fidelity of teleportation. We study resonant and non-resonant cases.