Summary: In this paper we present the results of the direct numerical simulation of mixing of a passive scalar in a spatially developing free round turbulent jet. The Schmidt number used in the simulations is equal to 1.0 and the Reynolds number, based on the orifice diameter and velocity, is equal to \(2.0\times 10^3\). The primary objective of this paper is to consider the self-similarity of the jet in the far field. Having considered the self-similarity of the velocity in a previous publication, we concentrate here on the self-similarity of the concentration of the passive scalar. To this end we have considered the profiles of the mean concentration and its fluctuations, together with the concentration probability density function distribution. The results have been compared with various experimental data that have been published in the literature. In general, the results agree very well with the experimental data. The conclusion is that the mean concentration is self-similar in the far field. The profiles of the root mean square of the concentration fluctuations are not self-similar. Furthermore, it is shown that the turbulent Schmidt number is equal to 0.74, which agrees very well with experimental values.