We report high-pressure X-ray diffraction and electrical measurements of the topological insulator SnBi2Te4 at room temperature. The pressure dependence of the structural properties of the most stable phase of SnBi2Te4 at ambient conditions (trigonal phase) have been experimentally determined and compared with results of our ab initio calculations. Furthermore, a comparison of SnBi2Te4 with the parent compound Bi2Te3 shows that the central TeSnTe trilayer, which substitutes the Te layer at the center of the TeBiTeBiTe layers of Bi2Te3, plays a minor role in the compression of SnBi2Te4. Similar to Bi2Te3, our resistance measurements and electronic band structure simulations in SnBi2Te4 at high pressure suggest that this compound exhibits a pressure-induced electronic topological transition or Lifshitz transition between 3.5 and 5.0 GPa. Display omitted •Topological insulator SnBi2Te4 and its comparison with the parent compound Bi2Te3 under pressure.•Structural properties of the trigonal phase of SnBi2Te4 and ab initio calculations.•Resistance measurements and electronic band structure simulations of SnBi2Te4.•A pressure-induced electronic topological transition between 3.5 and 5.0 GPa.