Every practical way to make this trip, cheapest and simplest first.
From the arrivals hall follow the signs down to Gimpo International Airport Station and take Seoul Subway Line 9 eastbound. Stay on all the way to Bongeunsa Station — there is nothing to change. Leave by Exit 7 and walk through ASEM Plaza into COEX Mall. Board a regular train rather than an express, as expresses skip Bongeunsa.
about 45 min · about KRW 1,550 on a transport card, plus a small distance supplement · The simplest option from Gimpo, and the cheapest.
Take Seoul Subway Line 5 from Gimpo International Airport Station to Yeongdeungpo-gu Office Station, then change to Line 2 and ride round to Samseong Station. Come out at Exit 5 or 6 and follow the underground passage under Millennium Plaza into COEX.
about 64 min · about KRW 1,550 on a transport card · A good fallback if there is disruption on Line 9.
Taxi ranks are immediately outside both the domestic and international arrivals halls. Show the driver 코엑스 or the address 서울 강남구 영동대로 513. The route crosses the city, so allow extra time in the morning and evening peaks.
about 60 min · about KRW 40,000 in a standard taxi, about KRW 80,000 in a black deluxe taxi · Luggage, groups, or a tight meeting time outside the rush hour.
Gimpo Airport Station is served by four different lines, so check the platform signs for Line 9 before you go down — Lines 5, 9, the Airport Railroad and the Gimpo Gold Line all meet here.
Incheon Airport (ICN) → COEX, Samseong, Seoul →
Gimpo Airport (GMP) → COEX, Seoul →