In this study total inelastic differential cross section and related stopping power expressions for positron were obtained by using generalized oscillator strength model. The stopping powers of low atomic number targets and of some biological compounds for positrons were calculated over the energy range from 50 eV to 10 MeV. Calculations of the stopping powers (SPs) for some low atomic number targets: H 2 , C, N 2 , O 2, P and for biological compounds: C 5 H 5 N 5 (adenine), C 5 H 5 N 5 O (guanine), C 5 H 5 N 3 O (cytosine), C 5 H 6 N 2 O 2 (thymine), C 20 H 27 N 7 O 13 P 2 (cytosine-guanine), and C 19 H 26 N 8 O 13 P 2 (thymine-adenine), have been evaluated for incident positrons in the 50 eV-10 MeV energy range. A detailed comparison of the calculated results with the other theoretical and experimental data for these target materials were presented. The calculated results of stopping powers for positrons in energy range from 50 eV to 10 MeV were found to be in good agreement to within 5% above 100 eV energies with other theoretical results.