We have made a new survey for dense cloud cores in the Orion B region using the NANTEN telescope. Two molecular transitions, the J = 1-0 line of (HCO+)-C-13 and the J = 1-0 line of (CO)-O-18, were used to study the distribution of dense molecular gas with densities Of 10(4)-10(5) cm(-3). We detected 19 (CO)-O-18 clumps, and the mass and the size of the C 180 clumps ranged from 13 M. to 990 M. and from 0.26 pc to 0.69 pc, respectively. Among the physical parameters of these (CO)-O-18 clumps, the molecular column density, N(H-2), has been found to be the best indicator of star formation; the molecular column density averaged within a (CO)-O-18 clump shows a good correlation with the IRAS luminosity as L-IRAS/L. proportional to N (H-2) (cm(-2))(4.8+/-0.6) (C.C. = 0.96). We also detected 11 (HCO+)-C-13 Clumps, Whose mass ranges from a few M. to 480 M.. Five of the (HCO+)-C-13 clumps are of smaller mass, and show no indication of massive star formation; they were newly found in this survey. Five of the eleven (HCO+)-C-13 clumps are particularly massive with an average mass of similar to 200 M.. It is found that these massive (HCO+)-C-13 clumps exhibit active formation of massive stars, as indicated by associated protostellar IRAS point sources, whose luminosities are 10(2)-10(4) L..