Based on the derivation of series expressions for error function of complex argument ξ=x+iy, the methods for computation, to high accuracy, of plasma dispersion function Z and jts derivative Z' in the region |y|≤1, |x|≤10 have been given in this paper. Furthermore, the plasma dispersion function and the suitable methods for its computation are studied systematically in varisus regionsl of complex ξ Plane; the satisfactory results are obtained on VAX-11/750 computer; these results, the used methods and its accuracy have been disccused; the fundamental behavior of Z and Z' for y≥0 and y<0 have been discribed respectively in the paper.