Octave spanning all-normal dispersion supercontinuum generation (SCG) was experimentally demonstrated in a solid, suspended-core fiber (SCF) infiltrated with water. Replacement of air with water in the cladding air-holes leads to a dramatic modification of the dispersion profile of the fiber, significantly flattening the characteristic over the visible and much of the near-infrared wavelength range at normal values. In such a fiber infiltrated with water, all-normal dispersion supercontinuum was generated with the spectral coverage from 435 nm to 1330 nm using femtosecond pumping with the output peak power of 150 kW and 800 nm central wavelength. The SCF without water infiltration – air in the cladding region – had a zero-dispersion wavelength at 760 nm and enabled the generation of the anomalous dispersion dynamics-based SCG in the wavelength range from 450 nm to 1250 nm. We also numerically calculated the coherence of simulated supercontinuum pulses with one-photon-per-mode noise seeds and point out that the all-normal dispersion SCG in suspended-core fiber infiltrated with water has the potential for high temporal coherence, while the fiber without water infiltration shows gradual decoherence of generated supercontinuum pulses with increasing pump power, over similar peak power range.