In the recent decades, different kinds of fiber materials are used for improving the asphalt mixture performance. Meanwhile, different kinds of fiber are used excessively due to their desirable physical and chemical properties and their easier application. The main purpose of this research is to evaluate the characteristics of the asphalt mixture while using basalt fiber and glass fiber. In order to provide asphalt samples, these two types of fibers are used in different percentages. In this way, 42 samples (with different percentages of fiber and bitumen) were made using Marshal Hammer. In the next step, while constructing 63 asphalt samples using a gyratory device, then mix asphalt conventional tests include the determination of indirect tensile strength, moisture sensitivity test, and resilient modulus and creep tests performed. The results of this research indicate that using these two types of fibers increased the percentage of optimum bitumen and marshal resistance. At best, adding 0.1% glass fiber resulted in 13% increase in marshal resistance. Finally, ANFIS-GUI was used to estimate the experimental result and the feasibility of employing neural fuzzy network to predict the laboratory data have been evaluated.