In the context of computer experiments, metamodels are largely used to represent the output of computer codes. Among these models, Gaussian process regression (kriging) is very efficient see e.g Snelson (2008). In high dimension that is with a large number of input variables, but with few observations the estimation of the parameters with a classical anisotropic kriging becomes completely wrong. The number of the parameters to estimate is the same as the number of inputs and it implies that the space of the optimization becomes too big compare to the available informations. One way to overcome this drawback is to use the isotropic kernel which is more robust because it estimates not as many parameters. However this model is too restrictive. The aim of this paper is twofold. Our first objective is to propose a smooth kernel with as few parameters as warranted. We propose a kernel which is a tensor product of few isotropic kernels built on well-chosen subgroup of variables. The main difficulty is to find the number and the composition of groups. Our second objective is to propose algorithmic strategies to overcome the difficulty of finding the number and the composition of the groups. Four forward strategies are proposed. They all start with the simplest isotropic kernel and stop when the best model according to BIC criterion is found. They all show very good accuracy results on simulation test cases. But one of them is the most efficient. Tested on a real data set, our kernel shows very good prediction results.