Radiological protection against high-energy heavy ions has been an essential issue in the planning of long-term space missions. The fluence to effective dose conversion coefficients have been calculated for heavy ions using the particle and heavy ion transport code system PHITS coupled with an anthropomorphic phantom of the MIRD5 type. The calculations were performed for incidences of protons and typical space heavy ions--deuterons, tritons, 3He, alpha particles, 12C, 20Ne, 40Ar, 40Ca and 56Fe--with energies up to 3 GeV/A in the isotropic and anterior-posterior irradiation geometries. A simple fitting formula that can predict the effective dose from almost all kinds of space heavy ions below 3 GeV/A within an accuracy of 30% is deduced from the results.