In this work we present a numerical study on attenuation of the fundamental mode in a suspended-core photonic crystal fibre (SC-PCF) made of fused silica, when a biological layer with various thickness and complex refractive index is present on the struts supporting the core and the photonic cladding (channels) is filled with water. In such a fibre structure both the effective refractive index and the mode area increase nonlinearly with the refractive index and with the thickness of the bio-layer, that in turn causes the increase of the attenuation of the fundamental (highest-) mode. For the calculation wavelength of the increase is intensified when the refractive index of the bio-layer exceeds 1.42, what is usually the case when even thin bio-layer is concerned. It is shown that it is possible to use such a fibre as a label-free sensor of a certain bio-layer deposited on a functionalised inner surface of the fibre.