A thin film magnetic head and a disk storage system having a magnetic disk and the thin film magnetic head provided on a floating type slider. The thin film magnetic head has an upper magnetic core and a lower magnetic core, wherein the upper magnetic core and the lower magnetic core are made of an electroplated thin film having sufficient average crystal grain size. The upper magnetic core is made of a Ni—Fe alloy having Ni of 38 to 60 wt % and Fe of 40 to 62 wt %, and the crystal grain size is smaller than 500 Å.