I have achieved this by applying one locale to the default scope, and then specifying a different locale for the store or website scope.
1. Go to System > Configuration,
2. Select ‘Default Config’ in Current Configuration Scope at the top left,
3. go to General tab and expand Locale Options, if it’s not already expanded,
4. Select locale that you would like for your backend and Save Config,
5. Now select your Store or Site in Current Configuration Scope,
6. Untick ‘Use default’ next to locale, select locale that you would like for your frontend and Save.
Now your back-end and front-end should have different locales.
Don’t forget to refresh your cache to see the changes.