Due to high computation demand, slant total delays (STDs) determined by 3D ray tracing cannot be widely used in geodetic analysis. This study proposes a novel fast 3D ray tracing approach, named APM-3D, based on piecewise algorithm and strictly matched step size. It can produce more than 1000 rays per second with a single core PC, which satisfies the operational applications of slant delays in mapping function establishment and other areas. Comparisons have shown mm-level agreement in slant delays at 5° elevation angle between APM-3D and several algorithms presented by different institutes in a comparison campaign. APM-3D also exhibits better stability than the standard RK4 method. Further validation using a 3D ray tracing based on the Cartesian coordinate system and 2D ray tracing also indicates excellent agreement, while constant differences in geometric delays between 3 and 2D exist under complex weather conditions. With ERA5 reanalysis data, the characteristics of STD evolution are presented during a rainstorm that occurred on July 1–2, 2020, over Wuhan. [ABSTRACT FROM AUTHOR]