YBa2Cu3O7/La0.7Sr0.3MnO3 (YBCO/LSMO) heterostructures with different thicknesses of LSMO (dLSMO) were fabricated, and their electrical transport properties were investigated. It was found that for dLSMO ≤ 40 nm the LSMO films are non-magnetic insulators, and the YBCO/LSMO systems remain superconducting; while for dLSMO ≥ 50 nm the LSMO films become ferromagnetic metals, and the YBCO/LSMO systems lose their superconductivity, due to the strong proximity effect of ferromagnetism in LSMO. A new approach based on the proximity effect is proposed to measure the intrinsic normal-state resistivity below Tc for high-Tc cuprates.