In modeling spatial processes, second-order stationarity assumption is often made. However, for spatial data observed on a vast domain, the covariance function often varies over space leading to a heterogeneous spatial dependence structure and therefore requires nonstationary modeling. Among the classes of methods for modeling nonstationary process, spatial deformation is one of the prominent methods, assuming the nonstationary process has a stationary counterpart in the deformed space. In this paper, we propose an approach for nonstationary geostatistical modeling using space deformation when a single realization of the spatial process is observed. Our method is fundamentally based on aligning the local variograms, and the warping variability in the distance from each subregion explains the spatial nonstationarity. We then propose to use the multidimensional scaling to map the warped distance to spatial locations. To estimate the spatial deformation, we propose a nonparametric method and their performances are examined by simulation studies. For applications, we apply our method to real environmental data, estimate the deformed space and perform spatial prediction.