The second survey of the molecular clouds in 12CO (J = 1-0) was carried out in the Large Magellanic Cloud by NANTEN. The sensitivity of this survey is twice as high as that of the previous NANTEN survey, leading to a detection of molecular clouds with M_CO > 2 x 10^4 M_sun. We identified 272 molecular clouds, 230 of which are detected at three or more observed positions. We derived the physical properties, such as size, line width, virial mass, of the 164 GMCs which have an extent more than the beam size of NANTEN in both the major and minor axes. The CO luminosity and virial mass of the clouds show a good correlation of M_VIR propto L_CO^{1.1 +- 0.1} with a Spearman rank correlation of 0.8 suggesting that the clouds are in nearly virial equilibrium. Assuming the clouds are in virial equilibrium, we derived an X_CO-factor to be ~ 7 x 10^20 cm^-2 (K km s^-1)^-1. The mass spectrum of the clouds is fitted well by a power law of N_cloud(>M_CO) proportional to M_CO^{-0.75 +- 0.06} above the completeness limit of 5 x 10^4 M_sun. The slope of the mass spectrum becomes steeper if we fit only the massive clouds; e.g., N_cloud (>M_CO) is proportional to M_CO^{-1.2 +- 0.2} for M_CO > 3 x 10^5 M_sun. Comment: 54 pages in total, 18 figures (21 files) and 4 tables, to appear in Astrophysical Journal Supplement Series. A full color version with higher resolution figures is available at http://www.a.phys.nagoya-u.ac.jp/~kawamura/research/NANTEN_LMC_1_preprint_highres.pdf