I don't believe you can do this; I'm fairly certain that the user must have contribute to the List to be able to add an entry. You can, however, redirect on submission, so that they don't see your data. That won't prevent an ornery person from being able to possibly navigate back to your list if they're SharePoint savvy, but it will make it more difficult.
I believe you can give them contribute only on the list, then not allow them permission to the site, so they can submit the form, be redirected elsewhere, and not be able to get back. But you can test this method.
There are many ways you can achieve this but it depends on your requirements:
- You can change the redirection setting in your submit/cancel button and in the form settings. This way users will not be redirected to the list data. This depends on how sensitive your data is as users if they had the list data link they will still be able to view the content.
- You can also create views and set permission on the view itself so users will not be able to view your list data.
- You can also change the permission of the user after they submit the form by creating a workflow that does that but be careful with Item level permissions, it can be tricky and messy.
- You can also add JavaScript code to your list data page that redirects whoever access it to another page
As far as I know, users do need contribute permission to be able run workflows and add items.
Read and write permission can be used to add items.
These are my suggestions let me know what works best for you.
Hi Ahmed,
Do you mind if users can see the items they have created but cannot see items that others have created? If so, this setting might work for you - found in List Settings | Advanced.

Cheers,
Chris
Thank you Shaikha and Chris for your replies, were really helpful;
Regards;
Ahmed
Hello,
you can add a new form in the list using SharePoint designer. Edit this page and add a web part called Nintext form web part. After adding this go to edit web part -> Put the form mode to 'New' -> Enter List id and Content Type Id of list. Now take the URL of this form and add a link either on Quick launch or other location.