The invention provides an anisotropic acoustic velocity measurement device of rock samples with fractures. The device comprises a high pressure reactor, a rubber sleeve and acoustic wave transducers,the high pressure reactor comprises a reactor body upper cover and a reactor body base, the cylindrical rubber sleeve comprises an upper end plug, a lower end plug and a sample chamber in the middle of the rubber sleeve, a rubber sleeve holder and the rubber sleeve positioned on the rubber sleeve holder are arranged on the reactor body base, extension columns are arranged on two sides of a peripheral horizontal line of the rubber sleeve, and the acoustic wave transducers are arranged in the extension columns and used for detecting the wave velocity of transverse waves and longitudinal waves ofthe rock samples. The device has the advantages that the velocity of the transverse waves and the longitudinal waves of the samples with the fractures in different directions are simultaneously measured, requirements for the shapes of the transducers are lowered, and measurement efficiency is greatly improved.