What is the maximum amount I can transfer to my daughter who stays in singapore as a gift from me. Will my daughter have to pay tax on that amount?

I can't speak to what the tax consequences for your daughter might be in Singapore, but as for US tax consequences:

1. Your daughter has no US tax consequences, regardless of the size of the gift.

2. You can give her up to $13,000 per year with no tax issues at all. This is the amount of the annual gift tax exclusion. If you're married both you and your husband can each give $13K, or $26K total per year, without any tax issues.

3. If you give more than $13,000 in a calendar year you will have to file a gift tax return with the IRS, but no gift tax is actually due unless the total of all gifts you've made that have exceeded the annual gift tax exclusion for all years exceeds the lifetime exclusion amount $5 million.

I need some details.

Are YOU a U.S. citizen or resident alien? Is your daughter?

Note that I can only advise you on U.S. tax issues.