Outgoing Mayor Keith Hightower was term-limited in 2006, after having won election in both 1998 and 2002. Glover defeated the Republican mayoral candidate, former city attorney Jerry Jones, in the general election held on November 7, 2006, by a 54-46 percent margin. The third-place contender, former broadcast journalist Liz Swaine, had been eliminated in the nonpartisan blanket primary held on September 30. Glover was formerly a member in both the Louisiana House of Representatives (1996–2006) and the Shreveport City Council (1990–1996).
In the primary held on October 2, 2010, Glover sought a second term against seven opponents. He led with 16,376 votes (45 percent), and city council member Bryan Wooley, a Republican, trailed with 11,218 votes (31 percent). In the November 2 general election, Glover handily defeated Wooley, 37,699 votes (64 percent) to 21,021 (36 percent).
On October 24, 2008, Glover vetoed a pay raise proposal that would have included all law enforcement personnel. This was the first veto the mayor used during his term. The pay raise, backed by a Shreveport City Councilman would use funds re-allocated from the current budget. The proposal had intended to remedy the city's number of law enforcement personnel that were leaving because of low pay and safety issues. Shreveport has a considerably higher crime rate and pays its police officers less than the regional average. The Councilman argued that the proposal was one way to retain more officers, saying: "Officers are leaving at an alarming rate to find better pay somewhere else. Let's keep it in the police department. Let's give the police officers a well deserved-well needed raise and lets make ourselves competitive in the marketplace." Glover responded by saying that the city only loses officers at a rate of 6 percent, which is below the national average of 10 percent.
Four days after the veto, supporters of the proposal failed to override it when the City Council voted in favor of the Mayor's decision. The supporters would have needed at least five votes to override.