Phase transition from normal- to inverse-spinel structure has been observed for $Fe_xCo_{3-x}O_4$ thin films as the Fe composition (x) increases from 0 to 2. The samples were fabricated as thin films by sol-gel method on Si(100) substrates. X-ray diffraction measurements revealed a coexistence of two phases, normal and inverse spinel, for $0.76{le}x{le}0.93$. The normal-spinel phase is dominant for $x{le}0.55$ while the inverse-spinel phase for $x{ge}l.22$. The cubic lattice constant of the inverse-spinel phase is larger than that of the normal-spinel phase. For both phases the lattice constant increases with increasing x. X-ray photoelectron spectroscopy measurements revealed that both $Fe^{2+}$ and $Fe^{3+}$ ions exist with similar strength in the x=0.93 sample. Conversion electron $Mddot{o}ssbauer$ spectra measured on the same sample showed that $Fe^{2+}$ ions prefer the octahedral $Co^{3+}$ sites, indicating the formation of the inverse-spinel phase. Analysis on the measured optical absorption spectra for the samples by spectroscopic ellipsometry indicates the dominance of the normal spinel phase for low x in which $Fe^{3+}$ ions tend to substitute the octahedral sites.