A Gwen Stefani fan is tracking her every move, lying in wait outside her parents' house, and leaving creepy letters and gifts for her ... according to a restraining order filed by Gwen's dad.
Dennis Stefani filed docs requesting protection from a man named Richard Portnoy -- who Dennis says has popped up outside his home and Gwen's home 3 times -- twice in February and once last week.
Dennis says he and his wife are terrified Portnoy will show up at their house again ... especially after one bizarre run-in. He says Portnoy made face-to-face contact with him at his house, and read a letter to him about his feelings for Gwen.
Even creepier, Gwen's dad says Portnoy has information about when and where Gwen gets medical treatments -- and attempted to make contact with her during an appointment on March 16.
TMZ broke the story ... police responded to the medical office and tried to locate Portnoy, but came up empty. Dad doesn't say anything about how Portnoy is getting intel on Gwen and the family ... but says they have no prior relationship.
Dennis was granted the restraining order -- which protects Gwen, Gavin Rossdale, their 3 kids ... plus Dennis and his wife Patricia. Portnoy has to stay 100 yards away from them, and have no contact.