The ERS said the first-past-the-post system to elect MPs takes no account of how big their majorities are or how many voted for losing candidates.
The society said this meant they were "wasted" votes and the system was "fundamentally broken".
The UK government said it had no plans to change the voting system.
The Electoral Reform Society (ERS) estimated 1,063,610 votes out of the total of 1,575,814 cast in Wales at the 2017 general election on 8 June were "wasted".
Campaigners said the votes were made up of 746,269 votes for losing candidates and 317,341 votes in excess of the number needed to elect the winning candidates.
It noted that Labour won 70% of seats with under half the vote, while the Tories gained vote share but lost seats.
With big Labour majorities at Aberavon, Merthyr Tydfil and Rhymney, Cynon Valley and Cardiff Central, campaigners claimed more than 80% of votes in those seats had no impact.
The society also claimed nearly a quarter of Welsh voters had been forced to vote tactically on the grounds their preferred party or candidate had no chance of winning the local seat.
ERS Cymru director Jess Blair called for a new electoral system which more closely reflected the proportion of votes cast for each party.
"This report reveals a picture of a voting system which is fundamentally broken," she said.
"There are a wide range of systems where votes are not thrown on the electoral scrapheap.
"We need to move towards a means of electing our MPs where people's voices are properly heard and where people don't feel forced to hold their nose at the ballot box."
A spokeswoman for the Cabinet Office, who set electoral rules, said: "First Past The Post is a voting system that offers a robust method of electing MPs.
"A referendum on changing the voting system for General Elections was held in 2011 and the public voted overwhelmingly in favour of keeping the First Past the Post system."
More than a million votes - two-thirds of the total - had "no impact" on the general election result in Wales, the Electoral Reform Society has claimed.