A large scale 12C16O (J=2-1) survey of the inner a few hundred parsecs of the Galaxy has been conducted using the University of Tokyo-Nobeyama Radio Observatory 60 cm survey telescope. We have taken about 700 12C16O (J=2-1) spectra in the region -2.5 deg <= l <= 2.5 deg and |b|<=1 deg with 0.125 deg grid spacing, covering the entire region of the huge molecular cloud complex in the Galactic center. We refer to the CO (J=1-0) data taken with the Columbia 1.2 m telescope and calculate the J=2-1 to J=1-0 intensity ratio. Velocity channel maps and longitude-velocity maps of CO (J=2-1) line are presented with corresponding maps of J=2-1/J=1-0 intensity ratio. Large scale CO maps enable us to identify several giant molecular cloud complexes and many characteristic features of molecular gas. We identify 15 molecular cloud complexes larger than 30 pc in our CO (J=2-1) data. Their virial masses are at least an order of magnitude larger than the masses estimated from the CO luminosity. This discrepancy can be removed if we notice that they may not be gravitationally bound but be in pressure equilibrium with the hot gas and/or magnetic field in this region. Using the expressions of virial mass and CO mass for a cloud in pressure equilibrium case, we get the X-factor for the Galactic center molecular clouds as X = 0.1E20 cm-2 (K km s-1)-1, which is an order of magnitude lower than that in the Galactic disk (X0 = 3.0E20 cm-2 (K km s-1)-1). We estimate the total molecular mass in the Galactic center as M(H2) = 1E7 Mo as a lower limit; the actual total gas mass within the central 400 pc of the Galaxy must be M(H2) = (1-6)E7 Mo. We diagnose the physical conditions of the molecular gas in the Galactic center using the intensity ratio between the J=2-1 and J=1-0 lines. Although the CO J=2-1/J=1-0 line intensity ratio is high ( 0.74) in the midplane, molecular gas at |b| > 0.25 deg exhibits low J=2-1/J=1-0 ratios ( 0.6). The overall J=2-1/J=1-0 luminosity ratio is R(2-1)/(1-0) =0.64+-0.01 if we include all the emission within |b| <= 1 deg, -2.5 deg <= l <= 2.5 deg, and |VLSR| <= 150 km s-1. This indicates that low density gas >= 50 pc away from the plane dominates the total CO luminosity of the central 400 parsecs of the Galaxy. The fractional distribution of the molecular gas with R(2-1)/(1-0) for each cloud complex clearly demonstrates the close relationship between the gas with very high ratio (R(2-1)/(1-0) >= 1.0) and associated UV sources.