A high-strength galvanized steel sheet contains C: 0.010% or more and 0.06% or less, Si: more than 0.5% and 1.5% or less, Mn: 1.0% or more and 3.0% or less, P: 0.005% or more and 0.1% or less, S: 0.01% or less, sol.Al: 0.005% or more and 0.5% or less, N: 0.01% or less, Nb: 0.010% or more and 0.090% or less, and Ti: 0.015% or more and 0.15% or less, on a mass percent basis. The Nb and C contents of the steel satisfy the relation of (Nb/93)/(C/12)