In computer experiments, the true function (scalar output) may be known to be monotone with respect to some or all input variables. In previous works, a methodology based on discrete - location approximation was developed by (Da Veiga and Marrel, 2012). (Golchi et al., 2013) used an approach similar to (Riihimaki and Vehtari, 2010) placing the derivatives information at specified input locations, by forcing the derivative process to be positive at these points. In this paper, we propose a new methodology based on Gaussian process metamodeling to sample from posterior distribution including monotonicity inform ation. Our method insures the monotonicity not only in a discrete subset of [0,1] but in the whole domain. By using a functional basis, we build a finitedimensional Gaussian process Y N such that all conditional simulations satisfy the monotonicity constraint over the whole domain. In figure (1), we show some simulated paths of Y N conditionally to given data (output values) and monotonicity information. By a Monte Carlo technique, the conditional mean value of Y N is computed and satisfies the monotonicity constraint. The so -called conditional monotone Kriging variance and confidence bounds are calculated as well.