We carried out the first wide-area unbiased survey with the ASCA satellite in the 0.7-10 keV band around a north Galactic-pole region covering a continuous area of 7 deg(2) (Large Sky Survey; LSS. To make the best use of ASCA's capabilities, we developed a new source-detection method in which the complicated detector responses are fully taken into account. Applying this method to the entire LSS data independently in the total (0.7-7 keV), hard (2-10 keV), and soft (0.7-2 keV) bands, we detected 107 sources altogether, with sensitivity limits of 6 x 10(-14) (0.7-7 keV), 1 x 10(-13) (2-10 keV), and 2 x 10(-14) ergs s(-1) cm(-2) (0.7-2 keV), respectively. A complete list of the detected sources is presented. Based on detailed studies by Monte Carlo simulations, we evaluated the effects of the source confusion and accurately derived the log N-log S relation in each survey band. The log N-log S relation in the hard band is located on the extrapolation from Ginga and HEAO1 results with a Euclidean slope of -3/2, while that in the soft band is consistent with the results from ROSAT. At these flux Limits, 30% +/- 3% of the CXB in the 0.7-7 keV band and 23% +/- 3% in the 2-10 keV band have been resolved into discrete sources. The average spectrum of faint sources detected in the total band shows a photon index of 1.63 +/- 0.07 in the 0.7-10 keV range, consistent with the comparison of source counts between the hard and soft energy bands. Those detected in the hard band show a photon index of 1.49 +/- 0.10 in the 2-10 keV range. These spectral properties suggest that the contribution of sources with hard energy spectra becomes significant at a flux of 10(-13) ergs s(-1) cm(-2) (2-10 keV). The most plausible candidates are type II active galactic nuclei, as indicated by on-going optical identifications.