John Moylett, aka Johnnie Fingers, claims he wrote the music and some of the lyrics for the 1979 song but was pressured into not taking credit at the time, reports The Irish Mail on Sunday.
Now he alleges he composed the majority of the music while Geldof wrote most of the lyrics, according to his new lawsuit.
The pianist is seeking a portion of the royalties accumulated over the years.
In response, Live Aid hero Geldof insists he played the song with the rest of the band, including Moylett, in a recording studio in London several days after returning from America and hearing the news about 16-year-old Brenda Spencer, who opened fire in California school playground, killing two people.
When asked why she carried out the shooting, she replied, "I don't like Mondays."