Please give me a list of web hosting companies (5-10) that provide
ASP, MS SQL server and online credit payment service. For online
credit card payment service, the web host should be secured enough to
store customer's credit card information and do the validation and
transaction.

I can't give you all list but check out http://www.spaceforhost.com
http://www.spectrum.net.in etc. I'll get a complete and more accurate
list later. It is slighlty difficult ot get ASP/MySQL combination. A
good place to search for would be http://www.freewebspace.net which
provides long list

All of the below are well-known established companies that should be
trustable and are offering what you need.

rackspace.com
media3.net
dellhost.com
interland.com
intermedia.net

I do not know at what stage your online credit card transaction
knowledge is, but I do want to point out that looking for one hosting
provider and a separate payment processor service, is often a good
thing.