Give me suggestion about backup of schema and full backup in oracle I need your help about backup in oracle database. Currently I am using Export Utility of Schema Backup but taking more time to complete and size is 40GB.

For full database backup using Image Copy and taking time more than 15 hours to complete and size is 650GB.

Which backup method is best for schema backup and full database backup which take less time and less size.

Database version Oracle Database 11gR2

Regards
650*1024/15/3600 = 12.3 MB/s. Sounds like you have a 100 Mbit network connection for backup. In that case, using a compressed backupset instead of image copy will significantly reduce the time it takes to backup the database. – Balazs Papp