Recent demonstrations of magnetization switching induced by in-plane current in heavy metal/ferromagnetic heterostructures (HMFHs) have drawn great attention to spin torques arising from large spin-orbit coupling (SOC). Given the intrinsic strong SOC, topological insulators (TIs) are expected to be promising candidates for exploring spin-orbit torque (SOT)-related physics. Here we demonstrate experimentally the magnetization switching through giant SOT induced by an in-plane current in a chromium-doped TI bilayer heterostructure. The critical current density required for switching is below 8.9 x 10(4) A cm(-2) at 1.9 K. Moreover, the SOT is calibrated by measuring the effective spin-orbit field using second-harmonic methods. The effective field to current ratio and the spin-Hall angle tangent are almost three orders of magnitude larger than those reported for HMFHs. The giant SOT and efficient current-induced magnetization switching exhibited by the bilayer heterostructure may lead to innovative spintronics applications such as ultralow power dissipation memory and logic devices.