One effective method for suppression of coupling from guided optical modes into cladding modes in an optical fibre Bragg grating is to use cladding mode suppression fibre.In this specially engineered fibre,the grating is written into the core and the inner cladding,both of which are photosensitive.A theory is presented in this paper to analyse the spectral characteristics of this kind of gratings.A fibre Bragg grating was experimentally fabricated with this kind of photosensitive fibre(PS-RMS-50 from StockerYale).It is shown both theoretically and experimentally that such gratings exhibit strong suppression of the coupling between core mode and cladding mode.The experimental result is in good agreement with the theoretical analysis.