In response to social demand, this paper investigates the breakeven price (BP) and potential electricity supply of nuclear fusion energy in the 21st century by means of a world energy and environment model. We set the following objectives in this paper: (i) to reveal the economics of the introduction conditions of nuclear fusion; (ii) to know when tokamak-type nuclear fusion reactors are expected to be introduced cost-effectively into future energy systems; (iii) to estimate the share in 2100 of electricity produced by the presently designed reactors that could be economically selected in the year. The model can give in detail the energy and environment technologies and price-induced energy saving, and can illustrate optimal energy supply structures by minimizing the costs of total discounted energy systems at a discount rate of 5%. The following parameters of nuclear fusion were considered: cost of electricity (COE) in the nuclear fusion introduction year, annual COE reduction rates, regional introduction year, and regional nuclear fusion capacity projection. The investigations are carried out for three nuclear fusion projections one of which includes tritium breeding constraints, four future CO2 concentration constraints, and technological assumptions on fossil fuels, nuclear fission, CO2 sequestration, and anonymous innovative technologies. It is concluded that: (1) the BPs are from 65 to 125 mill kW−1 h−1 depending on the introduction year of nuclear fusion under the 550 ppmv CO2 concentration constraints; those of a business-as-usual (BAU) case are from 51 to 68 mill kW−1h−1. Uncertainties resulting from the CO2 concentration constraints and the technological options influenced the BPs by plus/minus some 10–30 mill kW−1h−1, (2) tokamak-type nuclear fusion reactors (as presently designed, with a COE range around 70–130 mill kW−1h−1) would be favourably introduced into energy systems after 2060 based on the economic criteria under the 450 and 550 ppmv CO2 concentration constraint, but not selected under the BAU case and 650 ppmv CO2 concentration constraint, and (3) the share of electricity in 2100 produced by the presently designed tokamak-type nuclear fusion reactors (introduced after 2060) is well below 30%. It should be noted that these conclusions are based upon varieties of uncertainties in scenarios and data assumptions on nuclear fusion as well as technological options.