The union commissioned the online Angus Reid poll of 796 people, and said it suggests 74 per cent of respondents support Sunday openings, while 72 per cent call for extended shopping hours.
The BCGEU, which is trying to compete with private liquor stores, said the survey also suggests 64 per cent of respondents want new public liquor stores opened as a way to add cash to government coffers.
"Government stores offer lower prices, better selection, good customer service, convenience and better wages in communities all across the province," union president Darryl Walker said Sunday.
The province runs 197 liquor stores across, and 22 of them are open on Sundays.
Walker said opening every store on Sundays would generate up to $100 million a year, but the province disputes that would be the case.
"To be clear, opening additional government liquor stores on Sunday will simply cannibalize existing sales and will only generate $8.11 million additional revenue," Finance Minister Kevin Falcon said in a statement.
The BCGEU is currently embroiled in a contract dispute with the government, and talks broke off in June.
A wage hike and privatization of the Liquor Distribution Branch are among the main issues involved for more than 25,000 union members.
In early July, liquor store employees staged a one-day strike at three liquor distribution centres in Vancouver, Kamloops and Victoria.
The government has offered a two per cent wage increase in the first year of a two-year contract, and 1.5 per cent in the second year.
But the union wants 3.5 per cent in the first year and a cost-of-living increase in the second year.
Falcon defended the government's position.
"Government has offered a fair wage increase of 3.5 per cent over two years, and given the increasingly uncertain economic climate, I would encourage the union to come back to the bargaining table so a deal can be reached," he said.
The poll was conducted for the union between July 10 and 12, and the margin of error is plus or minus 3.5 per cent.