Amazon now ships to Singapore for free if your orders are above US$125 through its new initiative called AmazonGlobal Saver Shipping.
About FREE AmazonGlobal Saver Shipping
With FREE AmazonGlobal Saver Shipping, you receive free shipping to India and Singapore if your order includes at least US$125 of qualifying merchandise, excluding the Import Fees Deposit, gift-wrap charges, duties, and taxes. Most products shipped using the AmazonGlobal Program that are sold by Amazon.com are eligible for AmazonGlobal Saver. Items 20 pounds (9kg) or more, certain oversize items, e-documents, software downloads, music downloads and gift cards don’t qualify.