A stainless steel wire having a flux core for welding zinc-based alloy coated steel sheet having an outer metal sheath coating a core of flux wherein in total having in mass (%) as percentage to the total mass of the wire: C: 0.01-0.05%, Si: 0.1-1.5%, Mn: 0.5-3.0%, Ni: 7.0-10.0%, Cr: 26.0-30.0%, wherein an F value defined as a function of the above components ranges from 30 to 50, the flux further having a slag formation agent in mass (%) as percentage to the total mass of the wire: TiO2: 0.6-2.6%, SiO2: 1.8-3.8%, ZrO2: 1.0-3.5%, and optionally Al2O3: 0.1-1.0%, wherein the slag formation agent in total is less than 10%, and the wire further containing Fe and residual impurities.