Here, we calculated theoretically the positron bulk lifetime of cuprous halide (except CuI,which has not the blende structure) and some borides with the method of atomic superposition approximation (ATSUP) on the basis of the theory of local density approximation (LDA) and general gradient approximation (GGA),the calculated results are in good agreement with the experiment. On the other hand, the positron lifetime of many other compounds which have blende structure are calcualted,and the results agree with the results published in literatur. Here we take the CuCl as an example,the pictures of the electron potential energy distribution, probability density of positron and positron annihilation rate are given. Finally the systematic results were fitted with curve as a function of lattice constants, and the fitted results are compared with the outcomes of other articles.