H I spatial power spectra were determined for a sample of 24 nearby dwarf irregular galaxies selected from the Local Irregulars That Trace Luminosity Extremes-The H I Nearby Galaxy Survey sample. The two-dimensional power spectral indices asymptotically become a constant for each galaxy when a significant part of the line profile is integrated. For narrow channel maps, the power spectra become shallower as the channel width decreases, and this shallowing trend continues to our single channel maps. This implies that even the highest velocity resolution of 1.8kms-1 is not smaller than the thermal dispersion of the coolest, widespread H I component. The one-dimensional power spectra of azimuthal profiles at different radii suggest that the shallower power spectra for narrower channel width is mainly contributed by the inner disks, which indicates that the inner disks have proportionally more cooler H I than the outer disks. Galaxies with lower luminosity (MB > -14.5mag) and star formation rate (SFR, log(SFR (M ⊙ yr -1)) < -2.1) tend to have steeper power spectra, which implies that the H I line-of-sight depths can be comparable with the radial length scales in low-mass galaxies. A lack of a correlation between the inertial-range spectral indices and SFR surface density implies that either non-stellar power sources are playing a fundamental role in driving the interstellar medium turbulent structure or the nonlinear development of turbulent structures has little to do with the driving sources. © 2012. The American Astronomical Society. All rights reserved.