John Davies says more needs to be spent on marketing the project, which is heavily backed with public money.
Take up in areas that have had it for a year is 19% with just over £300,000 spent on marketing, which is around 1% of the overall cost so far.
But ministers said take up was where they expected it to be at this stage.
The Welsh government signed the deal - the largest of its kind in the UK - with BT in 2012 to roll out super fast broadband across Wales.
Download speeds of up to 80 megabits per second (Mbps) are being offered to domestic customers, compared to the average download speed currently available in Wales of around five to six Mbps. Even faster speeds are available to businesses.
The project, called Superfast Cymru, aims to ensure that 96% of homes in Wales are covered by 2016 and is seen as vital for Welsh businesses in an increasingly competitive global market.
Welsh ministers are spending £58m on the scheme, with a similar amount coming from the UK government and £90m from European funding.
In two years, the aim is for around 700,000 premises to have access but so far it has gone past the 150,000 mark.
Mr Davies, who chairs the Welsh advisory committee for the communications watchdog Ofcom, said the project was transformative but more needed to be done to make people aware of when it is rolled out in their communities to encourage demand for the high-speed broadband.
He said: "For small and medium sized businesses, it gives them an opportunity to compete on equal terms with businesses elsewhere in the UK and elsewhere in the world, and on the back of that they should be able to cut their costs and increase their revenues."
He added: "There is undoubtedly take up, there are undoubtedly benefits accruing now.
"The question is, if more is done on the stimulation side, can those benefits come through faster?"
In a statement the Welsh government said: "We are at an early stage in the programme and the marketing activity.
"Current take up figures for cabinets that have been in place for over one year are around 19%.  This is where we would expect take up to be at this stage."
Wales is not making the most of a £425m contract to roll out superfast broadband in rural areas, according to the former head of BT in Wales.