In Newer version of Magento2, it has been resolved. but in your Magento version You need to overwrite controller "vendor/magento/module-newsletter/Controller/Subscriber/NewAction.php"
and put below code just after line 122 $this->validateEmailAvailable($email);
$subscriber = $this->_subscriberFactory->create()->loadByEmail($email);
if ($subscriber->getId()
&& $subscriber->getSubscriberStatus() == \Magento\Newsletter\Model\Subscriber::STATUS_SUBSCRIBED
) {
throw new \Magento\Framework\Exception\LocalizedException(
__('This email address is already subscribed.')
);
}
to know about how to overwrite controller in Magento2, you can take reference of this link.