A court martial in Bulford, Wiltshire, found that the serviceman - known only as Marine A - shot the insurgent, who was armed with an AK47, in the chest with a 9mm pistol in Helmand Province more than two years ago.
Two other Marines - referred to as Marines B and C - were acquitted.
All will remain anonymous until the court martial or a judge decides otherwise.
The three men had denied murdering the unknown captured Afghan national on or about September 15, 2011, contrary to Section 42 of the Armed Forces Act 2006.
But a seven-strong board, consisting of officers and non-commissioned officers, convicted Marine A following a two-week trial.
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