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We have proposed a dispersion compensation scheme that uses a high-resolution arrayed-waveguide grating (AWG). When the diffraction order of the AWG is 59 and the number of waveguides in an arrayed-waveguide is 340, the calculated maximum second- and third-order dispersion compensation range is 18.0 ps/nm and /spl plusmn/6.0 ps/nm/sup 2/, and 1100 ps/nm and /spl plusmn/937.5 ps/nm/sup 2/, for a 1 ps-pulse and a 12.5 ps-pulse, respectively. In experiments, second-order dispersion (-0.8 to +5.2 ps/nm) is effectively compensated for 1,1-ps pulses; and. Pulse compression by third-order dispersion compensation is successfully demonstrated.