We present a robust single-photon quantum secret sharing (QSS) scheme with phase encoding in three-party implementations and a design way of more parties over a 50 km single-mode fiber network using a single QSS protocol. This scheme automatically provides perfect compensation for birefringence. A high visibility of 99.4% is obtained over three hours in visibility and stability measurements without any system adjustments, showing good potential for practical systems. Furthermore, polarization-insensitive phase modulators are realized using this system.