Let G=(V,E) be a graph with vertex set V and edge set E. The k-colouring problem is to assign a colour (a number chosen in {1,...,k}) to each vertex of G so that no edge has both endpoints with the same colour. The adaptive memory algorithm is a hybrid evolutionary heuristic that uses a central memory. At each iteration, the information contained in the central memory is used for producing an offspring solution which is then possibly improved using a local search algorithm. The so obtained solution is finally used to update the central memory. We describe in this paper an adaptive memory algorithm for the k-colouring problem. Computational experiments give evidence that this new algorithm is competitive with and simpler and more flexible than the best known graph colouring algorithms.