A method for manufacturing a tyre includes forming a carcass structure, forming a tread band, placing the tyre in a curing mould, and moulding and curing the tyre. The carcass structure includes a crown portion defined between two axially opposed sidewalls that extend radially toward an axis of rotation of the tyre and terminate in a circumferential portion comprising an annular reinforcing structure for mounting the tyre on a rim. The tread band extends circumferentially around the carcass structure and includes a moulded relief pattern. Forming the tread band includes producing a strip of elastomeric material and winding it onto the crown portion. The strip includes an elongated right cross-section that is asymmetrical in a transverse direction. The strip is wound in a plurality of axially consecutive turns until the tread band is formed. At least one turn is at least partly overlapped onto a previously deposited, axially consecutive turn.