Timothy Chu, 27, was on a dive with the Ogden Point Dive Centre at Race Rocks, southwest of Victoria, on Sunday when he failed to surface.
A search on Sunday and Monday failed to find any trace and efforts were suspended by Tuesday,
But the family believes the former British soldier may still be alive, and has launched an online petition urging both Canadian and U.S. officials to continue the search.
On the petition his brother Joshua Chu says Timothy is "skilled in survival and no stranger to challenge, having served in the British Army and named soldier of the year in 2011. We believe there is high hope that Timothy is still alive and must be found ASAP."
"Given the powerful current and miles of coastline on both Canadian and U.S. sides, [Chu's family] also ask anyone finding signs of the diver to contact police and email firstname.lastname@example.org."
Race Rocks are at the most southerly tip of Vancouver Island and are subject to extremely strong tidal currents.
Google Maps: Race Rocks, B.C.