You need to be more specific as to what the laptop needs to cater to. You also need to state a budget otherwise we'd be suggesting you buy an Apple MacBook with the highest of specs. Please read this and stylize your thread accordingly.
The appropriate suggestions will depend on the tools you will be using. E.G. if you are designing using WordPress or Joomla, then a low-end laptop will be OK, since those are web-hosted tools. If you will be using Adobe Creative Suite, then you will need something meatier.
Thanks for your valuable suggestion.Now my finally decision,I'm looking to buy Asus laptop . But I'm living in Bangladesh. my budget 50000 Thousand taka.According to my knowledge, Star Tech is a good website in Bangladesh. But what's model of laptop would be better? please help me Spinachy