Transmutation of minor actinides (MAs) is an effective solution to reduce the long-term radiotoxicity of nuclear waste. Online refueling and no fuel rod fabrication in thorium-based molten salt reactors (TMSR) are two remarkable advantages of MA transmutation. However, MA solubility limit of the fuel salt and the neutron spectrum in the core are two key parameters that have a strong impact on MA transmutation capability. In this paper, three types of carrier salt with different MA solubility limits and various salt volume fractions (SVFs) are introduced in a TMSR core to evaluate the MA transmutation characteristics. The results indicate that the Flibe salt with the best neutron economy can obtain the highest MA transmutation rate (TR), while the Flinak salt with the largest MA inventory can achieve the highest specific MA transmutation consumption (STC). STC and TR for the case with the Flibe salt and 5% SVF are about 200 kg/GWth.yr and 82%, respectively, which indicates that it can consume the annual MA yields from about 3.37 typical pressurized water reactors (PWRs). Meanwhile, the STC and TR for the case with the Flinak salt and 40% SVF are about 366 kg/GWth.yr and 75%, respectively, which indicates that it can consume the annual MA yields from about 50 typical PWRs. In addition, the total radiotoxicity of MAs after 50-year operation in TMSR can be lowered by as high as about 50%. The significant production of Pu isotopes can be reused as nuclear fuel in fast reactors. In particular, Pu-238, with the mass fraction of more than 60% in Pu isotopes, is a useful material for many nuclear applications. In conclusion, it is feasible to transmute MAs in TMSR and thus achieve the goals of reduction of MA's long-term radioactive hazards.