Three-dimensional structured illumination microscopy (3D-SIM) is a wide-field super-resolution technique in fluorescent imaging that can double the resolution beyond its classical limit. We introduce, to the best of our knowledge, a new 3D reconstruction algorithm based on the Richardson-Lucy deconvolution. The 3D-SIM imaging principle and the reconstruction steps are demonstrated in detail. Microspheres and biological specimen are used to present the performance of this method. The background of the out-of-focus portion is effectively suppressed, and true optical sectioning and super-resolution can be achieved simultaneously. For the custom-built 3D-SIM and this reconstruction algorithm, the measured resolution was 99.5±5 nm laterally and 294±9 nm axially.