I want to ask that if it is possible to copy the cookie from other computer to my computer.
Cookies can be intercepted, spoofed etc.
Still, unless you need a high level of security, they should be ok.
scoppc's method involves generating a hash from the given information, and storing it as a cookie.
If someone obtains the username, level and that hash, he/she will have access.
Conversely, if someone obtains the username, level and knows the additional strings concatenated, then he/she will be able to generate the hash and use it.
the security lies in that in order to access, one must know the hash (since obtaining username and level is relatively trivial).
However, to get this hash, one must either get the cookie, or know the strings (e.g. the keyword) used while generating it.
even if someone does obtain a hash from a user's cookie, he/she is unlikely to obtain the exact method of generating more hashes of that kind, since finding a hash collision is unlikely.
checking the database for matching username/password is also acceptable, and you would do that at least once (i.e. for login)
still, doing that for each access is, as scoppc noted, a little expensive for the limited security anyway.
if you really need security, you'll have to use strong encryption, perhaps with technologies such as SSL or your own system with say the mcrypt library.