We study in this paper an approximation method for the calculation of various performance measures of a GI/G/1 queue. We analyze the idle-period distribution as the starting point. The result is then taken as input to many known results to get other performance measure. We show that the distribution of the GI/G/1 idle period satisfies a nonlinear integral equation. This equation directly leads to an accurate approximation solution of the idle-period distribution of the GI/G/1 queue where the interarrival times have a generalized hyperexponential distribution (GH).