We have studied the average spectra of the Cosmic X-ray Background (CXB) and the field-to-field difference of the CXB spectral parameters, mainly utilizing the ASCA GIS. We created the average CXB spectrum from the ASCA Large Sky Survey (LSS) observations, which was carried out at the region around (l, b) = (75.40° 83.40°) covering the large continuous sky of ~1° × 5° with 76 pointings and 515 ks exposure. In the 2 - 10 keV energy band, the spectrum is well fitted with the power-law model (PLhard) which is almost consistent with the HEAO-1 A2. However, there exists a clear soft-excess below ~ 1.2 keV, which can be fitted with the steep power-law (PLsoft) of Γ ~ 6 or the 1-solar Raymod-Smith model of kT ~ 0.3 keV. Although this model appears to resembles the ROSAT measurements in the 0.5 - 1.5 keV energy band when unfolded, we cannot find the component of Γ= 2.1 which ROSAT reported. We also created the CXB spectra in 13 fields at high Galactic latitude with eliminating the discrete sources brighter than ~ 2×10-13 erg s-1 cm-2, and fitted them with the PLhard+PLsoft model. The 2 - 10 keV fluxes of PLhard are consistent with constant within the 90%-confidence upper-limit of 9%, while the 0.5 - 2 keV fluxes of PLsoft, most part of which is probably the Galactic origin, vary from field to field.