Physical model optimisation has frequently been complemented by experimental design in scientific research. However, it can be time consuming to perform real-world experiments and difficult to find affordable experimental designs. Bayesian optimisation based on the Gaussian process model has attracted extensive attention in the field of experimental design because it can build a good surrogate model and generate a sequential design simultaneously. However, it can create problems if researchers have a weak understanding of the system’s overall trend. This study introduces gradient information and proposes a new framework for constructing surrogate models: GRAdient-enhanced SEquential SUrrogate MOdelling (GRASE-SUMO). First-order gradient information is utilised as a guidance for selecting sampling space, and second-order gradient information is then adopted as an objective function in Bayesian optimisation. GRASE-SUMO is designed to mimic system changes and allows general system trends to be easily identified without a high level of prior knowledge. Experiments were conducted to verify the accuracy and stability of GRASE-SUMO, which works especially well in dealing with plate-shaped or valley-shaped response surfaces. When applied to laser-proton acceleration, GRASE-SUMO succeeded in rectifying and expanding the suitable conditions for optimal acceleration using only 30 samples, while the conventional sampling method requires about 102-3 samples with only three variables.