A novel web-like microstructure optical fiber (MOF) is fabricated which serves as a bundle of suspended submicron-thickness membranes as planar waveguides and their Y-type connection nodes as the secondary cores. The polarization dependent visible continuum coverage from 350 to 1 000 nm is generated from a 20-cm-long membrane of 0.55-μm-thickness pumped by 200-fs laser at 800 nm. We also obtain narrowband signal of blue dispersive wave around 410 nm with the up-conversion efficiency routinely beyond 20% in the Y-type secondary core in another smaller web-like MOF.