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.
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 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 for next season 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.