There is no separate entrance fee charged for the Rio Grande Wild & Scenic River; however, if you are planning to float the portions of the Wild & Scenic River inside Big Bend National Park, you will be charged for entry into the National Park.
A backcountry permit is required for all river use. Day-use river permits are free, while overnight or multi-day river trips have a permit fee of $10.
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Additional information can be found at Big Bend National Park's Fees & Reservations page.
