We have carried out an H^13^CO^+^(J=1-0 at 86.75433GHz) core survey in a large area of 1deg^2^, covering most of the dense region in the Orion B molecular cloud, using the Nobeyama 45m radio telescope with the 25-BEam Array Receiver System. We cataloged 151 dense cores using the clumpfind method. The cores have mean radius, velocity width, and mass of 0.10+/-0.02pc, 0.53+/-0.15km/s, and 8.1+/-6.4M_{sun}_, respectively, which are very similar to those in the Orion A cloud. We examined the spatial relation between our H^13^CO^+^ cores and the 850um cores observed by Johnstone and colleagues in 2001 (Cat. J/ApJ/559/307) and 2006 (Cat. J/ApJ/639/259), and found that there are two types of spatial relationships: H^13^CO^+^ cores with and without the 850um cores. Since the mean density of the 850um cores is higher than that of the H^13^CO^+^ cores, we can interpret the H^13^CO^+^ cores with 850um cores as being more centrally concentrated and hence more evolved, compared with those without.