The invention relates to a method for producing paper, board or the like. The method comprises obtaining a thick stock comprising cellulose fibres, forming a fibrous web and drying of drying the fibrous web. A strength agent system, which comprises at least one synthetic or natural polymer, or their mixture, and microfibrillated parenchymal cellulose material originating from non-wood sources, is added to the thick stock. The invention relates also to paper or board produced by the method.