Resuming on 165-6, 299 behind, Ned Eckersley (88) and Richard Jones (23) helped Leicestershire reach 259.
Following on, they made a poor start, with Liam Norwell (5-33) and David Payne (3-50) reducing them to 51-5 before Eckersley (85) again top-scored.
He could not prevent an innings and six runs defeat as they were out for 201.
It is second time Leicestershire have failed to take a Division Two game into the fourth day this season, after suffering a similar defeat by Nottinghamshire last week.
And they were outplayed once again, losing their first three wickets inside the first eight overs in both innings to effectively end their chances after Will Tavare's century helped Gloucestershire set an imposing total.
Eckersley batted well, receiving support from Ben Raine (42) and Clint McKay (29) in the second innings, but with Colin Ackermann unable to bat due to injury, Exckersley's wicket - Norwell's 10th of the match - ensured a second demoralising defeat inside a week.
Leicestershire slipped to a second County Championship defeat of the season as Gloucestershire took 14 wickets to complete a resounding win.