Project range and range distribution moments up to third order for twelve ion species implanted into five different substrates (such as amorphous A12O3, SiO2, UO2, LiNbO3 and 20/25/Nb stainless steel) are calculated using an improved nuclear scattering function developed recently. Some results are given for the ions considered with energy range from 5 keV to 1 MeV. The present theoretical results are compared with those published by Gibbons et al. and Winterbon, and our results are proved to agree with the recent experimental measurements more closely. The calculation method which deals with the range distribution moments in amorphous compounds and alloys is presented in some detail, and a brief discussion on the calculation accuracy is given.