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Cloud computing has been extending extensively, involving multiple users on the service it provides. Cloud based email is one of services provided by cloud computing with number of users expanding on yearly basis. Cloud computing faces concerning problem of security and privacy mainly based on its working environment. Identity authentication is one reliable method in cloud environment to identify users requesting for cloud services, currently user authentication in cloud computing is based on the credentials possessed by the user mostly username & password. However, this method has vulnerability of being compromised by illegitimate users when users’ passwords have been revealed or cracked. The paper proposes a more secure structure, i.e the two-factor authentication which authenticates by requiring the username/password pair also needs a second factor to completely grant access. The second factor is App stored in users’ smart devices. Username & password/Apps method will continue to allow users to set up passwords for their accounts, it will make a random compulsory code to be entered through App on smart phone devices hence keep privacy of cloud emails. Testing has been done with help of Python program environment. Comparing to recent related proposed schemes, our proposed scheme has advantage of high unbreakable security feature with low implement cost.