High-performance concrete (HPC) is a class of concretes that may contain more cementitious materials other than portland cement, such as fly ash and blast furnace slag, in addition to chemical admixtures, e.g., plasticizers. Strength, durability, and rheological properties of the normal concrete are enhanced in HPC. The compressive strength of HPC can be considered as a key factor to identify the level of its quality in concrete technology and the construction industry. This parameter can be directly acquired by experimental observations. However, testing methods are often time consuming, expensive, or inefficient. This article aims to develop and propose a new mathematical equation formulating the compressive strength of HPC specimens 28 days in age through a robust artificial intelligence algorithm known as linear genetic programming (LGP) using a valuable experimental database. The LGP-based model proposed here can be used for manual calculations and is able to estimate the compressive strength of HPC samples with a good degree of accuracy. The performance of the LGP model is confirmed through comparing the results with those provided by other models. The sensitivity analysis is also conducted, and it is concluded that the amount of cementitious materials, such as cement and furnace slag, have more influence than other variables.