On the basis of of local density approximation (LDA) and general gradient approximation (GGA), positron annihilation information has been calculated for five types of compound semiconductors, which are ZnO, GaN, GaAs, SiC and InP. The calculated information includes distribution of positron density, distribution of positron annihilation rate density, positron bulk lifetime, positron monovacancy lifetime and positron divacancy lifetime.