The fluence to organ-absorbed-dose and effective-dose conversion coefficients for heavy ions with atomic numbers up to 28 and energies from 1 MeV/nucleon to 100 GeV/nucleon were calculated using the PHITS code coupled to the ICRP/ICRU adult reference computational phantoms, following the instruction given in ICRP Publication 103 (2007 (Oxford: Pergamon)). The conversion coefficients for effective dose equivalents derived using the radiation quality factors of both Q(L) and Q(y) relationships were also estimated, utilizing the functions for calculating the probability densities of absorbed dose in terms of LET (L) and lineal energy (y), respectively, implemented in PHITS. The calculation results indicate that the effective dose can generally give a conservative estimation of the effective dose equivalent for heavy-ion exposure, although it is occasionally too conservative especially for high-energy lighter-ion irradiations. It is also found from the calculation that the conversion coefficients for the Q(y)-based effective dose equivalents are generally smaller than the corresponding Q(L)-based values because of the conceptual difference between LET and y as well as the numerical incompatibility between the Q(L) and Q(y) relationships. The calculated data of these dose conversion coefficients are very useful for the dose estimation of astronauts due to cosmic-ray exposure.