A common scientific purpose in spatial data analysis is prediction of a random field in unmeasured sites based on measured data in some sample sites. If the random field is Gaussian with parametric mean and covariance functions, optimal predictor and its mean square error can be determined. But in some applications, the data give evidence of non-Gausian features. In this case, if a nonlinear transformation of the random field is Gaussian, the spatial prediction is carried out. When the transformation is unknown, we assumed that it is belong to a certain parametric family of transformations. If the maximum likelihood estimators of the model parameters is determined and plugged in optimal predictor, optimality of the obtained predictor is doubt and, often, we can`t determine its MSE. Instead, in this paper, using the Bayesian approach, we determine the optimal predictor and its MSE. In a numerical example our method is used to deriving the Bayesian spatial prediction of rainfall at a given site.