Iceland competed at the 1964 Winter Olympics in Innsbruck, Austria.
Alpine skiing
Men
AthleteEventRaceTimeRankJóhann VilbergssonGiant SlalomDNF–Kristinn Benediktsson2:17.8661Árni Sigurðsson2:14.9056
Men's slalom
AthleteQualifyingFinalTime 1RankTime 2RankTime 1RankTime 2RankTotalRankKristinn BenediktssonDSQ–1:00.5727did not advanceÁrni Sigurðsson1:09.036559.6725 QF1:25.34401:13.78392:39.1239Jóhann Vilbergsson1:00.39461:02.2334did not advance
Cross-country skiing
Men EventAthleteRaceTimeRank15 kmBirgir Guðlaugsson1'04:53.967Þórhallur Sveinsson1'00:14.95530 kmBirgir Guðlaugsson1'54:00.364Þórhallur Sveinsson1'51:34.461
References
Official Olympic Reports Olympic Winter Games 1964, full results by sports-reference.com