State laws differ on the length of time which a suspension of driving privileges is recorded for on your driving record. The reason that your license was suspended will likely help determine how long it will be on your driving record.
For example in California, actions taken against your license, such as suspension or revocation due to a DUI or failure to show proof of insurance, is reported for 3 years from the proof termination date or the reinstatement date, whichever is earlier.
In Missouri, suspension for things such as Failure to Appear or Pay a Traffic Ticket (termed FACT) can only be removed after 5 years after the license reinstatement date. To remove it from the record, the DMV must be contacted with a request for the suspension to be removed.
When you have been convicted of an offense that resulted in the suspension of your license, that violation will be listed on your driving record for a certain amount of time. Besides waiting for the length of time your state has set for the suspension to leave your record, or requesting expungement of that offense from your record, it is unlikely that you could "fix" or get the suspension listing taken off your driving record.
To get specific answers for the state in which you are licensed, contact your local Department of Motor Vehicles.