In this paper, we investigate the entanglement and quantum teleportation of a two-qutrit state evolved under the one-axis counter-twisting Hamiltonian with the intrinsic decoherence effects. The entanglement and fidelity are analyzed as a function of decoherence rate, Hamiltonian coefficient and magnetic field. It is observed that the system is entangled all the times. The entanglement and fidelity are decreasing function of both decoherence rate and Hamiltonian coefficient. The magnetic fields optimize the negativity and fidelity effectively. We deduced that we can acquire some best fidelity for the system when it is entangled maximally.