The sentence is not wrong, but it sounds a little unnatural. I agree with Stephanie: "I love him unconditionally" is better.
In English, "unlimited" is a common word, but the adverb form "unlimitedly" is very uncommon.
2014년 8월 22일
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In your example I would use the word "unconditionally" to say you love the person without limits, without conditions, without bounds.