The viscosity of a typical endothermic hydrocarbon fuel (RP-3) at critical and supercritical conditions is measured using a novel viscosity measurement method by expanding the classical capillary method, and it can be applied to the viscosity measurement of single phase flow, including supercritical fluids. The measurement covers the temperature range of (298 to 788) K under pressures from (2.33 to 5) MPa. The uncertainty of the measurement is within +/- (2.14 to 6.42) % (k = 2) according to error analysis. The results are fitted as polynomials to analyze deviations. Out of 219 points, 205 points are within the +/- 5 % error band, which is 93.61 %. For all values, the average absolute deviation (AAD) is 2.01 %; the maximum absolute deviation (MAD) appears near the critical point, and the value is 8.83 %.