In this work we present an efficient algorithm which, with high probability, provides an almost uniform sample from the set of proper $\chi$-colourings of an instance of sparse random graphs $G_n,d/n$, where $\chi=\chi(d)$ is a sufficiently large constant. This work improves, asymptotically, the result of Dyer, Flaxman Frieze and Vigoda in \citeprevious-result where the algorithm proposed there needs at least $\Theta(\frac\log \log n\log \log \log n)$ colours.