user can not view nodes of custom content type I have created a user with the rights to view, edit and delete nodes of all the content types including some custom content types. On admin / content page it shows the list of contents of all content types except one custom content type. 

little edit Its showing the contents of that content type when I am adding the content from that user but not showing the contents of that content type posted as user1

When we try to filter the contents to banner content type it shows no results, when we filter the contents to other content types including some custom content types it shows the filtered list.

I checked the permission for that content type for the user role which was not defined earlier but even after granting the permissions its not showing up. 

After defining the permissions I have also rebuild the permission but the result is still the same.
I assume that you just forgot to publish the content. Since the first user has access to every content, he can see unpublished content from the userX, but userX cant see unpublished content created by user1. To change this behavior you could give userX the permission "bypass node access".

For further explanation take a look at the official documentation:

http://api.drupal.org/api/drupal/modules!node!node.module/group/node_access/7


  In determining access rights for a node, node_access() first checks whether the user has the "bypass node access" permission. Such users have unrestricted access to all nodes. user 1 will always pass this check.


Edit: As mentioned in the comment, although this solution solves the initial answer, in most cases it isn´t good to give the "bypass node access" to a large number of users. In the case which is described in the comment, you should use a more sophisticated module for content pushblishing like the Workflow Module.