In this research, the authors have developed an algorithm for predicting the compressive strength and compressive stress–strain curve of Basalt Fiber High-Performance Concrete (BFHPC), which is enhanced by a classical programming algorithm and Logistic Map. For this purpose, different percentages of basalt fiber from 0.6 to 1.8 are mixed with High-Performance Concrete with high-volume contact of cement, fine and coarse aggregate. Compressive strengths and compressive stress–strain curves are applied after 7-, 14-, and 28-day curing periods. To find the compressive strength and predict the compressive stress–strain curve, the Logistic Map algorithm was prepared through classical programming. The results of this study prove that the logistic map is able to predict the compressive strength and compressive stress–strain of BFHPC with high accuracy. In addition, various types of methods, such as Coefficient of Determination (R2), are applied to ensure the accuracy of the algorithm. For this purpose, the value of R2 was equal to 0.96, which showed that the algorithm is reliable for predicting compressive strength. Finally, it was concluded that The Logistic Map algorithm developed through classical programming could be used as an easy and reliable method to predict the compressive strength and compressive stress–strain of BFHPC.