A new approximation method for the plasma dispersion function Z(ζ) is presented. Multipoint quasi-rational approximation technique is used to find a bridge function that connects the power series and the asymptotic expansion of the function Z(ζ) using rational functions combined with exponential functions. An approximation with a polynomial of degree 10 is performed for the function Z(ζ), and the results obtained are compared with those of previous approximations from the literature. The results of this approximation were a relative error of ε = 0.0035 for Re[˜Z(ζ)] and a relative error of ε = 0.0011 for Im[˜Z(ζ)], which are lower than those of the other existing approximations