We demonstrate new types of dielectric-band photonic crystal lasers in a two-dimensional modified single-cell cavity with enlarged air holes. Finite-difference time-domain simulations performed in real and Fourier spaces show that the dielectric-band cavity modes originating from the first band edge point in the dielectric band have mode patterns that are distinguishable from conventional air-band cavity modes. In our experiment, the observed multimode lasing peaks are identified as the hexapole and the monopole dielectric-band cavity modes through the spectral positions and mode images. The thresholds of these lasers are measured as approximately 340 microW and approximately 450 microW, respectively, at room temperature. In addition, using the simulation based on the actual fabricated structures, quality factors and mode volumes are computed as 4900 and 1.09 (lambda/n)3 for the hexapole mode, and 4300 and 2.27 (lambda/n)3 for the monopole mode, respectively.