A high-strength hot-dip galvanized steel sheet and a method for manufacturing the steel sheet are provided. The high-strength hot-dip galvanized steel sheet has a specific composition including C, Si, Mn, etc. In this chemical composition, the content of Ti [Ti] and the content of N [N] satisfy [Ti]>4[N]. The high-strength hot-dip galvanized steel sheet has a microstructure including martensite at an area fraction of 60% or more and 90% or less, polygonal ferrite at an area fraction of more than 5% and 40% or less, and retained austenite at an area fraction of less than 3% (including 0%). The average hardness of the martensite is 450 or more and 600 or less in terms of Vickers hardness, and the average crystal grain diameter of the martensite is 10 μm or less. The standard deviation of the crystal grain diameters of the martensite is 4.0 μm or less.