Physical phenomena are observed in many fields (sciences and engineering) and are often studied by time-consuming computer codes. These codes are analyzed with statistical models, often called emulators. In many situations, the physical system (computer model output) may be known to satisfy inequality constraints with respect to some or all input variables. Our aim is to build a model capable of incorporating both data interpolation and inequality constraints into a Gaussian process emulator. By using a functional decomposition, we propose to approximate the original Gaussian process by a finite-dimensional Gaussian process such that all conditional simulations satisfy the inequality constraints in the whole domain. The mean, mode (maximum a posteriori) and prediction intervals (uncertainty quantification) of the conditional Gaussian process are calculated. To investigate the performance of the proposed model, some conditional simulations with inequality constraints such as boundary, monotonicity or convexity conditions are given.