The screening length of the charge-asymmetric electrolyte is calculated in the hypernetted chain approximation. Results are presented for 1.1, 2:1, 3:1, and 4:1 electrolyte with concentrations ranging from 10(-5) to 1 M. A number of analytic approximations for the screening length are compared to the hypernetted chain data. We find that the second moment approach of Attard [Phys. Rev. E 48, 3604 (1993)] gives good results for monovalent but not asymmetric electrolyte. A nonlinear version of the second moment approach is found to give good results for asymmetric electrolytes. We also find that the asymptotic formula of Mitchell and Ninham [Chem. Phys. Lett. 53, 397 (1978)], although giving a null result for monovalent electrolyte, is a satisfactory estimate for asymmetric electrolytes.