Alphabet Inc is listed as the most valuable equity holding of the church's USD 10 billion investment fund in 2015, although its exact value was not revealed.
Google is among a number of multinational companies which have been criticised for failing to pay enough tax, a practice that has been condemned in general by Archbishop of Canterbury Justin Welby.
"There has always been the principle that you pay the tax where you earn the money," the leader of the Church of England told the BBC last year.
In a foreword to the annual report, Welby says the church's "ethical and responsible investment" reflects its responsibilities to the common good of society.
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But the Times newspaper questioned whether the Google shareholding was compatible with church guidelines to confront companies that are accused of tax avoidance.
A spokesman told AFP that the church had "conducted engagement with a number of UK companies on corporate tax as part of an investor project to encourage good corporate practice".
He said: "We recognise the need for much more engagement beyond those interventions we have made to date."
The church announced last year that it would sell off 12 million pounds in holdings in thermal coal and tar sands, as part of a commitment to climate change.
It still has significant holdings in oil and gas giant BP but led a shareholder push to urge the company to be more open about how climate change could affect its business.