This is usually the problem with SSL certificate and the previous setting of a website that was not configured this way. You can try to use a plugins to fix this , such as - https://wordpress.org/plugins/wordpress-https/http://ithemes.com/codex/downloads/fix-ssl-non-ssl-links.zip however this does not guarantee fixing the issue.
Safer solution would be to remove the images that are causing this problem and to re-upload them.