To solve the problem that, in a wrapping cloth composed of obverse and reverse cloth pieces superimposed on each other (whole wrapping cloth), both the obverse and reverse cloth pieces are stuck to each other partially at many spots after washing/drying, and it has been difficult to neatly spread them respectively by a known cloth spreading machine.

The problem is solved by the following process: a wrapping cloth S is lifted to a predetermined height in such a state that both end corners of one side of the wrapping cloth S composed of obverse and reverse cloth pieces and provided with an opening in one edge thereof via which a bedding is to be put into/pulled out are gripped by a pair of chucks 21, the chuck-gripped parts of the wrapping cloth S are set apart from each other to spread the wrapping cloth S in a lifted state. In the above process, in such a state that the wrapping cloth S is lifted and spread left and right in an attitude so that the opening is directed downward, air is blown via the opening into between both the obverse and reverse cloth pieces to separate them from each other, thus neatly spreading them respectively.