Metamodels are widely used in the industry to predict the output of an expensive computer code. As the computer code involves a large amount of input variables, rather than directly creating one big metamodel depending on the whole set of inputs, industrials proceed sequentially, building metamodels depending on nested sets of inputs (the variables that are set aside are fixed to nominal values), i.e. the dimension of the input space is progressively increased. But at each step, the previous information is lost as a new Design of Experiment (DoE) is built to train the new metamodel. In this paper, an alternative approach is introduced, based on all the DoEs rather than just the last one. This metamodel uses Gaussian process regression and is called seqGPR (sequential Gaussian process regression). At each step n, the output is supposed to be the realization of the sum of two independent Gaussian processes Y n−1 + Z n. The first one Y n−1 models the output at step n − 1. It is defined on the input space of step n − 1 which is a subspace of the one of step n. The second Gaussian process Z n is a correction term defined on the input space of step n. It represents the additional information provided by the newly released variables. Z n has the particularity of being null on the subspace where Y n−1 is defined so that there is a coherence between the steps. First, some candidate Gaussian processes for the Z k are suggested, which have the property of being null on an infinite continuous set of points. Then an EM (Expectation-Maximization) algorithm is implemented to estimate the parameters of the processes. Finally the metamodel seqGPR is compared to a classic kriging metamodel where the output is assumed to be the realization of one second order stationary Gaussian process. The comparison is made on two analytic examples, one with two steps up to dimension 4, and the second one with three steps up to dimension 15. The introduced methodology is also tested on an industrial example that goes from dimension 11 to dimension 15. In all these test cases, seqGPR performs as good as or better than kriging.