For grid data, partially linear errors-in-variables models are constructed and studied. Large sample statistical inferences are made for the models as sample sizes of both two dimensions and one dimension tend to infinity respectively. For the modified least square estimators of the unknown parameters of the linear part and the variance of model error, their strong consistencies and convergence rates are obtained under weak conditions. For the spline function estimator of the unknown function of the nonlinear part, its strong consistency and convergence rate are obtained under certain conditions. Further, for the estimators of the parameters of the linear part and the variance of model error, their asymptotical normality are proved under some regularity conditions as sample sizes of two dimensions and one dimension tend to infinity respectively, and the asymptotical variances are provided.