You can take a flight, Nok Air, from Bangkok to Trang, and then a ferry to Koh Lipe. Another option is taking a flight, Air Asia, from Bangkok to Hat Yai, Bus to Pak Bara, and then ferry to Koh Lipe.
All the major cities of India like Mumbai, Delhi, Kolkata, Banglore, Ahemdabad are well connected to Bangkok via air. The popular airlines are Thai Airways, Air India, Indigo, Jet Airways, Air Asia. From Bangkok to Koh Lipe, you can choose from either of the options, Trang or Pak Bara.
You can take the Nok Air airlines from Bangkok to Trang, and then a ferry to Koh Lipe. Another time consuming option is taking the Air Asia island transfer package that includes flight from Bangkok to Hat Yai, bus to Pak Bara and ferry to Koh Lipe.
You can fly into Trang from Bangkok with Nok Air, or to Hat Yai from Bangkok with Air Asia, bus to Pak Bara, and then take a ferry to Koh Lipe. A few popular companies operating boat services are Adang Sea Tours, Tigerline Ferries, Forra Speedboats.
There are no cars on this island. There is a small concrete road that connects all the beaches. For that reason, the best way to explore this island is by foot. There are boats that can take you from one part of the island to another, or a few motorcycle taxis.
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