Can I become a Web Designer without programming?

I would recommend learning a bit of PHP. It's not as intense as C++. A lot of people have trouble getting their head around object oriented programming. I had a hard time myself and I was a programmer for a long time in C. PHP is more of a top down language, not as confusing and thus easier to learn. Get a book on C (without the ++) and learn that or just start with one of the many PHP books.

That said, there is a market surely for a good artist and web designer that can deal with HTML and CSS without programming, but it will limit your options.

yes it is possible to design web page without using programming language but it is not possible to create according to our thought.for using logical part in our web page programming language should be known.

yeah i think u can bt if u knw prograaming u can invent and rethink differntly and apply more ideas of creativity ....

IMO you'd better know a little programming knowledge, even if you can read them it is ok. Coz now nearly every site have dynamic side to meet the requiremen of visitors and clients, In a team for the site to be quality you must communicate with mate, so you must understand their work.