Hello 和仁 田中,

You might be using Professional edition trail org.

Did you sign up from below link for developer edition.

https://developer.salesforce.com/signup
 
I would suggest you sign up from above link and then try to create new apex class, 

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You're probably viewing it in the Production environment. You need to be in either a Sandbox or Developer Org to create new Apex classes. In production you are not able to create class or trigger.

Development Mode is not the same as your environment. You can be in Development Mode and be in Production.
 
1. Do you see in the upper right anything that says "Sandbox". You typically get a small text in upper right of browser which tells you which Sandbox you are in. If you don't see that then you are in a Production or Developer Edition Environment.
 
Go to Setup -> Data Management. Do you see an option for Sandboxes? If you do than you are in a Production org. Login to one of the Sandboxes to make your Apex Classes.
 
Checkout the Developer Guide Docuemntation on the developer.force.com, the deployment section, for more details.

I will suggest you to register for a developer account. It will give you full freedom to test almost all major feature of salesforce. Plus you can keep it as long as you want. 

http://www.developerforce.com/events/regular/registration.php?d=70130000000EjHb

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