The management of nuclear wastes has long been a problem that hinders the sustainable and clean utilization of nuclear energy since the advent of nuclear power. These nuclear wastes include minor actinides (MAs: Np-237, Am-241, Am-243, Cm-244 and Cm-245) and long-lived fission products (LLFPs: Se-79, Zr-93, Tc-99, Pd-107, I-129 and Cs-135), and yet are hard to be handled. In this work, we propose a scheme that can transmute almost all the MAs and LLFPs with a lead-cooled fast reactor (LFR). In this scheme, the MAs and the LLFPs are loaded to the fuel assembly and the blanket assembly for transmutation, respectively. In order to study the effect of MAs loading on the operation of the core, the neutron flux distribution, spectra, and the k(eff) are further compared with and without MAs loading. Then the LLFPs composition is optimized and the support ratio is obtained to be 1.22 for Np-237, 1.63 for Am-241, 1.27 for Am-243, 1.32 for Se-79, 1.53 for Tc-99, 1.02 for Pd-107, and 1.12 for I-129, respectively, indicating that a self-sustained transmutation can be achieved. Accordingly, the transmutation rate of these nuclides was 13.07%/y for Np-237, 15.18%/y for Am-241, 13.34%/y for Am-243, 0.58%/y for Se-79, 0.92%/y for Tc-99, 1.17%/y for Pd-107, 0.56%/y for I-129. Our results show that a lead-cooled fast reactor can be potentially used to manage nuclear wastes with high levels of long-lived radioactivity.