Accurately estimating and mapping vegetation cover for monitoring land degradation and desertification of arid and semiarid areas using remotely sensed images is promising but challenging in remote, sparsely vegetated and large areas. In this study, a novel method – geographically weighted logistic regression (GWLR – integrating geographically weighted regression (GWR) and a logistic model) was proposed to improve vegetation cover mapping of Kangbao County, Hebei of China using Landsat 8 image and field data. Additionally, a new method to determine the bandwidth of GWLR is presented. Using cross-validation, GWLR was compared with a globally linear stepwise regression (LSR), a local linear modelling method GWR and a nonparametric method, k-nearest neighbours (kNN) with varying numbers of nearest plots. Results demonstrated (1) the red and near infrared relevant band ratios and vegetation indices significantly improved mapping; (2) the GWLR, GWR and kNN methods led to more accurate predictions than LSR; (3) GWLR reduced overestimations and underestimations compared with LSR, kNN and GWR, and also eliminated negative and very large estimates caused by GWR and LSR; and (4) The maximum distance of spatial autocorrelation could be used to determine the bandwidth for GWLR. Overall, GWLR proved more promising for mapping vegetation cover of arid and semiarid areas.