NBGW currently receives £550,000 annually from the government, but has asked for an undisclosed increase in funding support to bring development plans to fruition.
David Hardy, editor of NBGW magazine Yr Ardd, said: "We have been going for 10 years and we are still very much finding our way, and as you can imagine there's now an increasing requirement for maintenance.
"I don't know if you can be 100 per cent confident about anything at the moment, but we have put in what our director described as a robust bid for further funding."
He added: "We are short of undercover space for corporate and education events and there's a plan attached to the permanent Plants for Health exhibition to expand it and add on a glasshouse.
"There's also a plan to redevelop our main public entrance and restaurant, and with all these projects we have to have assistance. There's a lot of scope here for developing the garden and the surrounding land, which is a national nature reserve and organic farm, but it needs a helping hand.
"We don't think we are really going to hear much before Christmas and as we are in the heritage ministry we are comparing like for like with other heritage organisations and attractions like museums and art galleries."