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delete access to a object's records.

I need to give access to a user to deleted records- I have provided Delete permission to profile on object permissions. When I am trying to delete the record it lets me delete one record type record but does not allow me to delete other record types by giving following error: 
nsufficient Privileges
You do not have the level of access necessary to perform the operation you requested. Please contact the owner of the record or your administrator if access is necessary. 

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Please help!
NagendraNagendra (Salesforce Developers) 
Hi Ruchi,

Please find the explanation below.

Restricting access:
The “Read,” “Create,” “Edit,” and “Delete” object permissions determine which actions a user can perform on any of the object's records to which they have access. Field-Level Security allows you to prevent certain users from seeing sensitive or confidential information contained in records they can see.
Opening up access:
 The “View All” and “Modify All” object permissions give users access to all of an object’s records, regardless of record-level access settings.
Record-level access (called “Sharing” in Salesforce) determines which records a user can see for a particular object, using the following tools:
  • Organization-wide defaults
  • Role hierarchy
  • Record-Level Access: Under the Hood Data Access in Salesforce
  • Territory hierarchy
  • Sharing rules
  • Teams
  • Manual sharing
  • Programmatic sharing

Because you have so many options for managing record-level access — and because some of these options are affected by organizational dependencies — determining which records users can access can quickly become complicated. Additionally, you might also be changing your sharing configuration frequently in response to new business requirements. This can trigger record access changes that ripple through your organization. These changes have an even greater impact in very large organizations, where it can take some time to recalculate access for a large number of users, and adjust the tables that record their access rights. For these reasons, it’s important to understand how Salesforce calculates and grants access at the database level.

For more information check with below link. Please mark this as solved if it's resolved.

Regards,
Nagendra.