This paper discusses the estimation and plug-in kriging prediction non-stationary spatial process assuming a smoothly varying variance an additive independent measurement error. A difference-based kernel estimator of the variance function and a modified likelihood estimator of the mea surement error variance are used for parameter estimation. Asymptotic properties of these estimators and the plug-in kriging predictor are established. A simula tion study is presented to test our estimation-prediction procedure. Our kriging predictor is shown to perform better than the spatial adaptive local polynomial regression estimator proposed by Fan and Gijbels (1995) when the measurement error is small.