Recently, a novel image scrambling (i.e., encryption) scheme without bandwidth expansion was proposed based on two-dimensional (2-D) discrete prolate spheroidal sequences (DPSS). This paper gives a comprehensive cryptanalysis of the image scrambling scheme, and draw a conclusion that it is not sufficiently secure against various cryptographical attacks, including ciphertext-only attack, known/chosen-plaintext attack and chosen-ciphertext attack. The cryptanalytic results suggest that the image scrambling scheme can only be used to realize perceptual encryption, instead of provide content protection for digital images.