Abstract: For Beijing ElectronPositron Collider Upgrade (BEPCⅡ), six pairs of current leads with four different currents were used for superconducting quadruple magnets (SCQ) and a pair of 4 000 A current leads were used for the superconducting solenoid magnet (SSM).Multi-tube current leads for SCQ and SSM magnets were designed. The special feature of the leads is that a copper block is added to the cold end of the leads to delay the time for runaway in case of the cooling helium being interrupted. The numerical simulation results on steady and unsteady thermal processes by CFD software package Fluent6.0 are also presented.