The recently discovered titanium-based kagome metal CsTi₃Bi₅, which exhibits superconductivity without an accompanying charge density wave, provides an ideal platform to investigate the intrinsic electronic structure and superconductivity. Moreover, it enables the exploration of superconductivity in the two-dimensional limit of the kagome lattice. Here, we systematically investigate the influence of biaxial mechanical strain (ε) on the electronic structure and superconductivity of monolayer CsTi₃Bi₅ using first-principles calculations. We demonstrate that the prominent van Hove singularity (VHS) at the M point can be monotonically tuned to the Fermi level by tensile strain. Furthermore, the superconducting transition temperature T_C exhibits a dome-shaped dependence on strain, reaching a maximum of 3.6 K at an optimal tensile strain of ε=+2%. The average superconducting gap magnitude is 0.35 meV, with an orbital-dependent and anisotropic distribution. Our results provide a detailed understanding of the superconductivity of monolayer CsTi₃Bi₅ and show that strain is an effective, continuous tuning knob for manipulating the electronic structure and superconductivity.