Radial profile measurement of Z(eff) using visible bremsstrahlung (5300 Å) in the Large Helical Device (LHD) has often encountered difficulties because the intensity profile was largely deformed by the nonuniform visible bremsstrahlung emissions from the edge ergodic layer surrounding the core plasma. A space-resolved flat-field extreme ultraviolet (EUV) spectrometer has been newly adopted to measure the Z(eff) profile using the EUV bremsstrahlung continuum in the wavelength range of 70-75 Å. The EUV bremsstrahlung intensity profiles have been measured and checked for all the magnetic configurations with totally different magnetic field structures in the ergodic layer of LHD. It is found that the nonuniform bremsstrahlung emission from the thick ergodic layer can be entirely eliminated by use of the EUV emission with relatively high photon energy of 170 eV. As a result, the Z(eff) profile can be successfully measured for most of discharges regardless of magnetic field structures of the ergodic layer. The Z(eff) profiles measured in the EUV range are compared with those measured in the visible range at a magnetic configuration with the thinnest ergodic layer thickness. The result verifies that the use of the EUV bremsstrahlung continuum is an alternative way for the Z(eff) measurement in toroidal plasmas with nonuniform bremsstrahlung emissions at the edge. Typical results from the EUV bremsstrahlung measurement are presented showing a fairly flat Z(eff) profile with error bars of ±14%.