B737-800
Flight Crew Air Transport Pilot (ATP)
Inflight Event / Encounter Wake Vortex Encounter
General None Reported / Taken
Environment - Non Weather Related; Procedure
Cruising at FL370 in smooth air; seatbelt sign off.  Encountered a moderate double bump that was quite violent that felt like wake. Immediately turned on seatbelt sign and called the FAs to see if anyone was hurt and fortunately everyone was ok.  Called ATC and asked if any aircraft were near us.  They told us we crossed 1;000 feet below a Super A380 that was 20 miles away to our right.  We told ATC we went through their wake. ATC thought the distance was sufficient.  The quartering tailwind of about 20 [KTS] kept the wake in our path and caused us to encounter the turbulence.  Not suspecting and having the seatbelt sign off could have easily caused injuries or aircraft upset at high altitude. Perhaps ATC should give more spacing during light winds and tailwinds to the lower crossing aircraft below a Super or at a minimum; issue an advisory.
B737-800 Captain reported encountering wake turbulence at FL370 from an A380 that was 20 miles away and 1;000 feet above them.