This sounds like you are restoring a database backup file (.BAK) rather than restoring a Transaction Log Backup file (.LOG) i.e. rolling a database foreward, from it's last FULL BACKUP, to a particular point in time.
Was the database, from which the original backup was taken, placed in the FULL Recover model and do you also have Transaction Log backups?
To qualify, a database backup file contains the database data at a specific point in time only. A database can only subsequently be rolled forward to a given point in time using Transaction Log Backups, sourced from the same database as the Full database backup.