The newly developed quasi-steady state (QSS) method to measure the thermal conductivity combines characteristic advantages of transient and steady-state techniques but avoids their major drawbacks. Based upon a transient hot strip setup, the QSS technique can be realized by adding only two temperature sensors at different radial distances from the strip. After a short settling time, the QSS output signal which is the measure for the thermal conductivity is constant in time as it is for steady-state instruments. Moreover, in contrast to transient techniques, the QSS signal is not altered by homogeneous boundary conditions. Thus, there is no need to locate a time window as has to be done with the transient hot wire or transient hot strip techniques. This paper describes the assessment of the QSS standard uncertainty of thermal conductivity according to the corresponding ISO Guide. As has already been done in previous papers on the uncertainty of the transient hot wire and transient hot strip techniques, first, the most significant sources of error are analyzed and numerically evaluated. Then the results are combined to yield an estimated overall uncertainty of 3.8%. Simultaneously, the present assessment is used as an aid in planning an experiment and in designing a QSS sensor to achieve minimal uncertainty. Such a sensor is used to verify the above mentioned standard uncertainty from a run on the candidate reference material polymethyl methacrylate.