A web winding apparatus comprises a cutter (T), a web pressing member (66a) and a roller (64) which are movable together between two bobbins (33, 43) supported respectively by two rotational center members (32, 42). The cutter (T) cuts a web (W) being transferred, the web pressing member (66a) presses an end portion of the web (W) cut with the cutter (T) on the bobbin (33/43) being empty, and the roller (64) transfers the web (W) being transferred to come, toward the bobbins (33, 43). The apparatus further comprises two peripheral covers (34, 44) independently turnable around the rotational center members (32, 42) and respectively covering parts of outer peripheral surfaces of the webs (W) wound on the two bobbins (33, 43). Each of the peripheral covers (34, 44) respectively having circumferential openings (34c, 44c) is turnable selectively to a first position to direct the circumferential opening (34c/44c) toward the roller (64) and a second position to partition the bobbin (33/43) side covered thereby and the roller (64) side.