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We report both experimentally and numerically that a flow-free pseudospin-dependent acoustic topological insulator (ATI) is realized by two honeycomb sonic crystals with direct and indirect band gaps. By simply rotating triangular rods of the sonic crystals, the band inversion is realized, which arises from the change of the coupling strength between the triangular rods and leads to a topological phase transition. Moreover, a direct band gap is converted into an indirect band gap when the rotation angle is larger than 32.18°. By using the triangular rods with the rotation angles of 0°, 30°, and 60°, we design two topological insulators which include a topological nontrivial sonic crystal with the direct band gap (30°) and the indirect band gap (60°), respectively. In the topological insulator composed of the sonic crystal with the indirect band gap, the pseudospin-dependent edge modes also support acoustic propagation, in which the clockwise (anticlockwise) acoustic energy flux emulates pseudospin− (pseudospin+) state. Furthermore, these edge modes are topologically protected and remain high transmission after transmitting through topological waveguides with defects. The results provide diverse concepts to design ATIs with versatile applications.