  We present high-pressure resistance measurements up to 40 GPa on recently
discovered titanium-based kagome metal CsTi$_3$Bi$_5$. At ambient pressure,
CsTi$_3$Bi$_5$ shows no evidence of superconductivity in resistivity and
specific heat. By applying pressure, superconductivity emerges and the
superconducting transition temperature ${\it T}_{\rm c}$ reaches its first
maximum of 1.2 K at $\sim$5 GPa. Then the ${\it T}_{\rm c}$ is suppressed by
pressure and cannot be detected around 10 GPa, manifesting as a superconducting
dome. Remarkably, upon further increasing pressure above $\sim$13 GPa, another
superconducting dome shows up, with the maximum ${\it T}_{\rm c}$ of 0.6 K and
ending pressure at $\sim$36 GPa. The variation of ${\it T}_{\rm c}$ displays a
clear double-dome shape in the superconducting phase diagram. Our work
demonstrates the similarity between CsTi$_3$Bi$_5$ and CsV$_3$Sb$_5$, providing
valuable insights into the rich physics of these novel kagome metals.
