As a logical next step in improving the radio-to-submillimeter spectral index as a redshift indicator, we have investigated a technique of using the entire radio-to-far-infrared spectral energy distribution (SED) for deriving photometric redshifts for dusty starburst galaxies at high redshift. A dusty starburst SED template is developed from the theoretical understanding of various emission mechanisms related to massive star formation processes, and the template parameters are selected by examining the observed properties of 23 IR-selected starburst galaxies: Td = 58 K, β = 1.35, and fnth = 1. The major improvement in using this template SED for deriving photometric redshifts is the significant reduction in redshift uncertainty over the spectral index technique, particularly at higher redshifts. Intrinsic dispersion in the radio and far-infrared SEDs as well as absolute calibration and measurement errors contribute to the overall uncertainty of the technique. The derived photometric redshifts for five submillimeter galaxies with known redshifts agree well with their spectroscopic redshifts within the estimated uncertainty. Photometric redshifts for seven submillimeter galaxies without known spectroscopic redshifts (HDF 850.1, CUDSS 14.1, Lockman 850.1, SMM J00266+1708, SMM J09429+4658, SMM J14009+0252, and FIRBACK J1608+5418) are derived.