Edge coupler is a key component of silicon-based optoelectronic chips, which dramatically reduces the coupling loss between fibers and transmission waveguides. Here, we propose an ultralow-loss three-step silicon edge coupler based on a 130 nm CMOS process. By replacing the silicon substrate with a material with a lower refractive index than silicon oxide, the silicon leakage loss and polarization-dependent loss can be significantly improved. This structure avoids the existence of a cantilever, which enhances the mechanical strength of the edge coupler. Coupling with standard single-mode fiber, the simulation results demonstrate that the TE/TM mode has an ultralow loss of 0.63/1.08 dB at 1310 nm and 0.57/1.34 dB at 1550 nm, and the 0.5 dB bandwidth covering the entire communication band is about 400 nm. In the entire communication band, the polarization-dependent loss is less than 0.8 dB. Furthermore, we propose a taper shape design method based on mode analysis, which can be adapted for any taper to improve its compactness. Compared with the parabolic shape, the coupling loss of the edge coupler with a length of 460 μm for the TE mode is improved by 0.3 dB on average, this edge coupler provides a feasible solution for fiber-to-chip coupling and is perfectly suitable for wavelength division multiplexing applications in optical communications.