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Cut the grapefruit peel in strips.
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Place in a pan and cover with cold water. Bring to a boil. Drain. Repeat for a total of four times to remove the bitterness from the peel.
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After boiling for the fourth time, place the peels back in the pan and top with 1/2 cup sugar.
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Add just enough water to cover the peels and bring to a simmer. Simmer for 1 1/2 hours on low heat.
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Place parchment or wax paper on a baking sheet and place a cooling rack on top.
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Transfer the peels to the cooling rack and allow to dry overnight.
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Toss with the remaining 1/4 cup of sugar.