Linear transformation with good branch number plays a significant role in designing components of symmetric key primitives. Linear transformation based on XOR of several rotations can be efficiently implemented, and has been widely used in the block ciphers such as SMS4, HIGHT and the hash functions SHA-2, MD6. Besides, if the linear transformation is involutional, it will facilitate the decryption process. In view of this, a kind of involutional linear transformation based on the XOR of several rotations was studied, the numeration of this kind of linear transformation was given and the branch number was shown to be upper bounded by 4. Meanwhile, the relationship between the parameters of the rotations and the branch number was discussed, which provides a theoretical basis for the design. 