More than 25% of the memberships sold so far have been purchased by new season ticket members, since the public sale commenced last month.
The club sold over 1,500 memberships for the last campaign.
The Warriors finished third in the RaboDirect PRO12 this season and qualified for the play-offs, which they narrowly lost 17-15 to Leinster in Dublin.
In the league the team scored 68 tries and were the top try scorers in the RaboDirect PRO12. Their tally was the third highest in a single season since the Celtic League was formed in 2001.
The club have re-signed 15 players for next season and three players have been signed, including Scotland international Richie Vernon, who is moving back to the club from English Premiership outfit Sale Sharks.
Existing season ticket members can renew their seats for next season until Friday 31 May at 5pm. All seats which have not been renewed by then will be released for general sale.
The club is holding an open day tomorrow (Thursday 23 May) from 12pm until 7.30pm and on Saturday 1 June from 11.30am until 2.30pm, where supporters can purchase season tickets in person and get a tour of the stadium. The British & Irish Lions game against the Barbarians will be shown live at Scotstoun on Saturday 1 June (kick-off 12.30pm).
Glasgow Warriors managing director Nathan Bombrys said: "The support we received last season was fantastic, which created a real home field advantage for our team.
"We are encouraged that our supporters have acted so quickly to get behind the team, and it's great to have so many new members already on board.
"It takes significant support to win competitions like the RaboDirect PRO12 and the Heineken Cup, and the support of our season ticket members is a vital part of our efforts to bring a major club trophy to Glasgow.
"We still have a long way to go to match the levels of support enjoyed by some of our competitors in France and Ireland, but our season ticket membership sales over the last month show that there is a growing appetite for Glasgow Warriors in the west of Scotland."
Season tickets can be purchased online at www.glasgowwarriors.org and from the ticket office on 0844 800 3490.
Guinness PRO12
Suite 208, Alexandra House,
The Sweepstakes
Ballsbridge, Dublin 4, Ireland