A linear time solution of the weighted feedback vertex problem for diamond graphs is the main contribution of this paper. The result can be obtained from a more general result [1]. There, it is shown that the regarded problem is a linear extended monadic second-order (EMS) extremum problem, and that all such problems can be solved in linear time for classes of graphs of bounded tree-width (see Bodlaender’s paper [2] for a linear-time algorithm for finding a tree decomposition if it is bounded by a fixed parameter). Since it is obvious that diamond graphs have bounded tree width, the result follows from this more general result. Related results can be found in another paper [3].