In this work, steered molecular dynamics simulations were performed to study the process of Na⁺, K⁺ and Cl^－ traversing through (6,6), (7,7), (8,8), (9,9) and (10,10) carbon nanotubes (CNTs). The potential of mean forces (PMF) of ions passing through CNTs were calculated with the umbrella sampling method. Ion hydration in CNTs and in bulk solution was analyzed and compared. Simulation results show that ions are hindered from entering narrow CNTs at the entrance|however, it is easy for ions to leave narrow CNTs into bulk solution at the exit. There is almost no hindrance for ions to translocate through wide CNTs. The free energy barriers for ions translocating through CNTs decrease sharply with the increase of diameter. Different free energy barriers of Na⁺, K⁺ and Cl^－ entering CNTs indicate that CNTs have an inherent ion selectivity. When ions traverse through CNTs, coordination numbers and preferential orientation of water molecules in coordination shells of ions are different from those in bulk, which determine the dehydration energies of ions and affect free energy barriers of ions traversing CNTs and the ion selectivity of CNTs. Studies on ions traversing through the hydrophobic pores of CNTs assist in understanding the function of hydrophobic regions of ion-channel proteins and provide guidance for the design of CNT-based nano- fluidic devices.