Bharatiya Janata Party leader Rajiv Pratap Rudy accompanied Paswan during the filing of papers in Hajipur, headquarters of Vaishali district, about 30 km from here.
He told the media he was confident of winning with a record margin.
"I will repeat my past world record," Paswan said. "People have been supporting me and will vote for me."
Paswan faces 93-year-old Janata Dal-United candidate and sitting member Ram Sunder Das, who is also a former chief minister.
Paswan's wife Reena Paswan and son Chirag Paswan were present at a public meeting he addressed soon after filing the papers.
The LJP joined the BJP-led National Democratic Alliance in February, after a gap of 12 years. The party is contesting seven parliamentary seats in Bihar.