The invention relates to a composition for sizing of a surface of paper, board or the like and its use for increasing strength properties of paper, board or the like. The composition has a solids content of 3-30%, and it comprises degraded non-ionic starch, and at least 0.5 weight-% of anionic polyacrylamide, which has a molecular weight, MW, >500 000 g/mol and <2 500 000 g/mol and an anionicity in the range of 4-35 mol-%. The invention further relates also to a method for producing paper, board or the like, which comprises addition of a first strength composition, which comprises a cationic agent, to a fiber stock, formation of a fibrous web from the fiber stock, drying of the fibrous web to dryness of at least 60%, and application of a second strength composition, which comprises an anionic hydrophilic polymer and a starch component, on the surface of the fibrous web.