The invention relates to the technical field of tunnel construction, in particular to a construction method of a subway shield tunnel crossing a prestressed anchor cable. The construction method comprises the following steps that construction preparation is made before a shield machine crosses the anchor cable, and a bin opening point is preset after the preparation is completed; then a jet grouting pile is used for reinforcement in an anchor cable area; a reinforced soil body for rotary jet grouting reinforcement is tested, after reinforcement meets requirements, shield tunneling is carried out, anchor cable crossing construction is carried out, and shield tunneling parameters are controlled and analyzed in the construction process; according to the excavation parameters, the bin openingpoint opening operation is reasonably selected, the anchor cable wound on a cutter head is removed, or a cutter is replaced; and after the bin opening operation is completed, shield tunneling construction is restored, and finally the shield machine crosses the anchor cable. The construction method is simple in process; the jet grouting pile reinforcement technology and the shield bin opening technology are relatively mature, the implementation efficiency is high, and the construction safety is ensured; and the basis and construction experience are provided for the subsequent process that a shield crosses the anchor cable, the anchor cable treatment success rate is improved, and the construction difficulty is reduced.