Non-equilibrium environment is one of the most common dissipative factors encountered in the application of quantum system. The dynamic evolution and steady-state solutions of two coupled qubits in both equilibrium and non-equilibrium environments are studied systematically. The results show that in the equilibrium bath, enhancing the coupling strength, increasing the energy detuning and raising the temperature of the heat bath are all beneficial to the enhancement of the entanglement. While in the non-equilibrium bath, the entanglement is enhanced (suppressed) with the increasing of the temperature gradient for the low (high) average temperature. In addition, the relationship between the heat current and the energy detuning, the coupling strength and thetemperature of bath is also studied. It is found that for the two qubits in two independent heat baths or in two common heat baths, the influence of parameters on the evolution of the system and the heat current is different. By selecting appropriate coupling strength, energy detuning and temperature gradient, the stable heat current between two heat baths can be obtained, so the steady-state entanglement of the system.