We obtain the rotational spectra for cyanopolyynes HC2n+1N (n = 0–8) and their cations through quantum chemical calculations. Rotational constants, quartic centrifugal distortion constants, and hyperfine constants are calculated. The rotational constants are determined at the theoretical level of B3PW91/cc-pVTZ, incorporating with the calibration for the moment of inertia. This significantly improves the accuracy with respect to the uncalibrated ones. Quartic centrifugal distortion constants are estimated using the empirical relation, achieving an accuracy of ∼0.02%with respect to the experiment. Hyperfine constants are computed at the B3PW91/6-311+G(df, pd) and B3PW91/aug-cc-pVTZ levels. The overall frequency characteristics of all the target molecules are discussed and their detectability in the interstellar medium is also quantitatively evaluated. The rotational spectra of selected species (HC13N, HC15N, HC17N, and HC5N+) are reproduced, showing satisfied consistency with experiments or observations. Our results provide useful reference for observations and experiments, even that more advanced calculation levels and basis sets are required to achieve better accuracy.