This paper presents a novel reaction microscope designed for ion-atom collision investigations, established at the Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou, China. Its time-of-flight (TOF) spectrometer employs an innovative flight-time focusing method consisting of two acceleration regions, providing optimal time focusing conditions for charged fragments with diverse initial velocities. The TOF spectrometer's axis intentionally tilts by 12° relative to the ion beam direction, preventing potential obstructions from the TOF grid electrodes. The introduced focusing method allows for a flexible time-focusing TOF spectrometer design without restricting the length ratio of the two regions. In addition, this configuration in our case significantly suppresses noise on the recoil ion detector produced by residual gas in the ion beam trajectory, which is a considerable challenge in longitudinal spectrometers. In a test experiment on the single electron capture reaction involving 62.5 keV/u He2+ ions and a helium atomic beam, the recoil longitudinal momentum resolution achieved 0.068 atomic units. This novel configuration and successful test run show excellent precision for ion-atom collision studies.