To reduce the environmental errors, a snapshot phase-shifting interference microscope (SPSIM) has been developed for surface roughness measurement. However, fringe-print-through (FPT) error widely exists in the phase-shifting interferometry (PSI). To ensure the measurement accuracy, we analyze the sources which introduce the FPT error in the SPSIM. We also develop a FPT error correction algorithm which can be used in the different intensity distribution conditions. The simulation and experiment verify the correctness and feasibility of the FPT error correction algorithm.