Hi Rajesh,

You can get the API enabled for Professional Edition but you will need to contact the Account Executive as this is an additional cost option for professional edition.

Salesforce provides programmatic access to your organization's information using a simple, powerful, and secure application programming interface, the Apex Web Services API (the API).

To use the API, your organization must be on one of the following 4 editions.  Note that this feature is enabled by default:

1. Enterprise Edition
2. Unlimited Edition
3. Developer Edition
4. Performance Edition

The API is not available by default for the following editions:

1. Contact Edition
2. Group Edition
3. Professional Edition

Note: Professional and Group Edition may have the API temporarily turned on by contacting their Account Executive.  Professional can also purchase the API as a feature by contacting their Account Executive.

Beginning in Winter '15 Release, API is not available to be activated for Contact Manager or Group Editions, not even for migration purposes.
Please contact your Account Executive if you would like to upgrade your edition to Enterprise or higher.

For Professional Edition organizations, all requests for API access must be purchased and can be processed contacting your Account Executive.

If you need the API enabled for a Data Migration to a Professional Edition organization, you will need to contact your Account Executive and request that API be provisioned as courtesy. These requests should be for Data Migrations only and will be up to you and your Account Executive to determine the time frame of the API enabled.

There may be applications on the AppExchange that are permitted for the Group or Professional Editions even though it states that it requires API.  
Those applications will require appropriate authentication to provide blanket API access. Please contact the Developer of the application to determine if this authentication has been provided.

Note: Certified partner applications, such as the PE version of the Excel Connector, are granted an API token once they have completed a security review. This API token is sometimes referred to as a "Client ID". API requests identified with a certified partner application's API token are allowed to operate with Professional Edition orgs. More information on Partner Certification can be found here: 
http://wiki.apexdevnet.com/index.php/Certification_FAQ.

Please mark this as best answer if this helps.

Best Regards,
Nagendra.P