The fantasy series is now the most-watched ever shown on Sky.
However, this was an improvement on previous year, when more than 50% opposed Mr Murdoch's reappointment.
The broadcaster said in a statement: "The board notes the significant vote against resolution 3, the directors' remuneration report, and resolution 12, the re-election of James Murdoch, and will continue to engage with shareholders to understand their views as part of its ongoing programme of engagement".
Game of Thrones helped Sky increase customer numbers by 51 per cent in the first quarter, as revenue and earnings also grew.
In response, Martin Gilbert, Sky's deputy chairman, pointed out that Sky's board had formed an independent committee to evaluate the terms of 21st Century Fox's takeover, which he said had met 11 times since the takeover approach was tabled in December a year ago.
Jeremy Darroch, Group Chief Executive, said that the good revenue growth and excellent profit growth was achieved against the backdrop of pressure on consumer spending and lower spend on United Kingdom television advertising.
Shareholder advisory groups - including Institutional Shareholder Services (ISS), Glass Lewis and Pirc - have called on investors to vote against his re-election at Sky's annual general meeting and also to rebel against what they claim are potentially "excessive" pay plans.
"We've had a strong start to our new financial year with good revenue growth and excellent profit growth", said chief executive Jeremy Darroch.
This week the Competition and Markets Authority (CMA) outlined how it will examine the deal and the impact on media plurality and broadcasting standards in the United Kingdom and invited submissions for the six-month investigation.
Fox owns 39.1% of Sky is trying to purchase the entire company in a deal worth $18.5 billion.
Mr Murdoch won 51% of votes cast by independent shareholders at the annual general meeting - up from 49% previous year.
Culture Secretary Karen Bradley sent the £11.7bn ($15.4bn) deal to the CMA for review last month following the conclusion of a three-month inquiry by Ofcom.
Ms Bradley referred the bid to the Competition and Markets Authority last month for a full-blown investigation, with the competition watchdog set to report back with its final recommendations next March.
Ms White gave evidence to the committee on Tuesday when she told MPs the regulator found "extremely disturbing" behaviour at Fox News when looking at the bid.