Uniaxial tensile tests of basalt fiber/epoxy (BF/EP) composite material with four different fiber orientations were conducted under four different fiber volume fractions, and the variations of BF/EP composite material failure modes and tensile mechanical properties were analyzed. The results show that when the fiber volume fraction is constant, the tensile strength, elastic modulus, and limiting strain of BF/EP composite material all decrease with increasing fiber orientation angle. When the fiber orientation angle is constant, the tensile strength, elastic modulus, and limiting strain of BF/EP composite material all increase with increasing fiber volume fraction. A certain degree of fiber clustering appears in the epoxy resin when the basalt fiber volume fraction is >1.2%. The fiber equidistribution coefficient and clustering fiber content were used to characterize the basalt fiber clustering effect. With the increase of fiber volume fraction, the clustering fiber content gradually increased, but the fiber equidistribution coefficient decreased. Meanwhile, based on Tsai theory, a geometric model and a tensile mechanical model of the clustering fiber are established. By considering the fiber clustering effect, the BF/EP composite material tensile strength is calculated, and the calculated values are close to the experimental results.