Structured illumination microscopy (SIM) has been a widely-used super-resolution (SR) fluorescence microscopy technique, but artifacts often appear in reconstructed SR images which reduce its fidelity and might cause misinterpretation of biological structures. We present HiFi-SIM, a high-fidelity SIM reconstruction algorithm, by engineering the effective point spread function (PSF) into an ideal form. HiFi-SIM can effectively reduce commonly-seen artifacts without loss of fine structures and improve the axial sectioning. Since results of HiFi-SIM are not sensitive to used PSF and reconstruction parameters, it lowers the requirements for dedicated PSF calibration and complicated parameter adjustment, thus promoting SIM as a daily imaging tool.