Using an ultra-high-energy (γ⩾1000) electron to collide with laser pulses to generate high-energy γ-rays is an important way to treat cancer. We investigate a method for modulating high-energy γ-rays with higher energy and more collimation using tightly focused circularly polarized laser pulses colliding with an ultra-high-energy electron. Theoretical derivation and numerical simulation within the framework of classical electrodynamics show that higher electron initial energy, stronger laser intensity, and a longer pulse can generate higher γ-ray energy. The high-energy γ-rays generated by an electron with higher initial energies are more collimated. The increase of the laser intensity and the increase of the pulse width will increase the angular range of the high-energy γ-rays. At the same time, the phenomenon of the "jumping point," in which the radiation energy varies with the laser intensity, was found. Our findings have important implications for modulating better high-energy γ-ray sources.