A flux cored wire for gas shielded arc welding, the flux being filled into a steel outer sheath, wherein a flux filling ratio is in a range of 10 to 25% by mass relative to the total mass of the wire, the flux contains acid-soluble Mg, the acid-soluble Mg is contained in a content of 0.05 to 1.0% by mass relative to the total mass of the wire, a content of the acid-soluble Mg in a first flux component having a particle diameter of 75 μm or less in the flux is set at 0.1 to 5% by mass relative to the total mass of the first flux component, a content of the acid-soluble Mg in a second flux component having a particle diameter of more than 75 μm and 106 μm or less in the flux is set at 0.1 to 7% by mass relative to the total mass of the second flux component, and a content of the acid-soluble Mg in a third flux component having a particle diameter of more than 106 μm in the flux is set at 1 to 15% by mass relative to the total mass of the third flux component, wherein the flux cored wire has a composition consisting of, relative to the total mass of the wire: 1 to 10% by mass of at least one of Ti and Ti compound(s) in total in terms of Ti; 0.030% by mass or less of P; 0.030% by mass or less of S; 0.05 to 1.0% by mass of at least one of Mg and Mg compound(s) in total in terms of Mg; optionally 0.5 to 2% by mass of at least one of Si and Si compound(s) in total in terms of Si; optionally 1.0 to 3.0% by mass of Mn; optionally 0.02 to 0.15% by mass of C; optionally 0.01 to 1.0% by mass of at least one of Al and Al compound(s) in total in terms of Al; optionally 0.05 to 0.5% by mass of at least one of Na compound(s), K compound(s) and Li compound(s) in total in terms of Na, K and Li, respectively; optionally 0.05 to 0.3% by mass of F compound(s) in terms of F; optionally 0.5% by mass or less of at least one of Zr and Zr compound(s) in total in terms of Zr; optionally 0.005 to 0.050% by mass of at least one of Bi and Bi compound(s) in total in terms of Bi; and optionally, at least one selected from the group consisting of: Cu: 0.5% by mass or less; Ni: 3.0% by mass or less; Cr: 0.5% by mass or less; Mo: 0.5% by mass or less; Nb: 0.2% by mass or less; V: 0.2% by mass or less; at least one of B and B compound(s): 0.0001 to 0.0100% by mass in total in terms of B; and rare earth metal(s)(REM(s)): 0.01 to 0.5% by mass, wherein a Fe content is 77% by mass or more, relative to the total mass of the wire, with the balance of the composition being alloying agents, optionally including one or more of Ca and Li, and compound(s) thereof, and inevitable impurities. 1 to 10% by mass of at least one of Ti and Ti compound(s) in total in terms of Ti; 0.030% by mass or less of P; 0.030% by mass or less of S; 0.05 to 1.0% by mass of at least one of Mg and Mg compound(s) in total in terms of Mg; optionally 0.5 to 2% by mass of at least one of Si and Si compound(s) in total in terms of Si; optionally 1.0 to 3.0% by mass of Mn; optionally 0.02 to 0.15% by mass of C; optionally 0.01 to 1.0% by mass of at least one of Al and Al compound(s) in total in terms of Al; optionally 0.05 to 0.5% by mass of at least one of Na compound(s), K compound(s) and Li compound(s) in total in terms of Na, K and Li, respectively; optionally 0.05 to 0.3% by mass of F compound(s) in terms of F; optionally 0.5% by mass or less of at least one of Zr and Zr compound(s) in total in terms of Zr; optionally 0.005 to 0.050% by mass of at least one of Bi and Bi compound(s) in total in terms of Bi; and optionally, at least one selected from the group consisting of: Cu: 0.5% by mass or less; Ni: 3.0% by mass or less; Cr: 0.5% by mass or less; Mo: 0.5% by mass or less; Nb: 0.2% by mass or less; V: 0.2% by mass or less; at least one of B and B compound(s): 0.0001 to 0.0100% by mass in total in terms of B; and rare earth metal(s)(REM(s)): 0.01 to 0.5% by mass, Cu: 0.5% by mass or less; Ni: 3.0% by mass or less; Cr: 0.5% by mass or less; Mo: 0.5% by mass or less; Nb: 0.2% by mass or less; V: 0.2% by mass or less; at least one of B and B compound(s): 0.0001 to 0.0100% by mass in total in terms of B; and rare earth metal(s)(REM(s)): 0.01 to 0.5% by mass, wherein a Fe content is 77% by mass or more, relative to the total mass of the wire, with the balance of the composition being alloying agents, optionally including one or more of Ca and Li, and compound(s) thereof, and inevitable impurities.