Abstract Despite the success of Gaussian processes (GPs) in modelling spatial stochastic processes, dealing with large datasets is still challenging. The problem arises by the need to invert a potentially large covariance matrix during inference. In this paper we address the complexity problem by constructing a new stationary covariance function (Mercer kernel) that naturally provides a sparse covariance matrix. The sparseness of the matrix is defifined by hyperparameters optimised during learning. The new covariance function enables exact GP inference and performs comparatively to the squared-exponential one, at a lower computational cost. This allows the application of GPs to large-scale problems such as ore grade prediction in mining or 3D surface modelling. Experiments show that using the proposed covariance function, very sparse covariance matrices are normally obtained which can be effectively used for faster inference and less memory usage.