Here is a few things you can do according to my checklist :

• Check your computer's date/time settings.That's the most common cause of certificate errors.
• Try clearing your browser's cache (and perhaps cookies too) and re-start your laptop.
• Have you tried disabling any browser add-ons or (for browser's like Firefox, chromium its common).
• Go to Settings->Account->Browser Connection and try both types: http and https
• Disabling Settings->Offline->Offline Mail if you are using it.
• Temporarily disabling your anti-virus scanner to see if the behaviour changes (Might be the antivirus firewall or Internet protection is at high make it to medium if you are using Kaspersky).

Hello Sachin,

There are few reasons why gmail shows network error :

• You must verify the email address and its validity. It can be done by Google search on your email address and checking out the result page it appears on.
• You must verify the browser & its latest updation. It can be the reason of showing network error.
• Firewall privacy setting can be a reason of showing network error. You can include gmail in privacy setting of the browser and allow third party cookie.
• You can add gmail.com to your browsers list of trusted Internet sites to resolve error.
• The most common issue associated with network error is when browser get stuck in infinite loop. An outdated/corrupted cookie, or settings that are preventing the appropriate cookies from saving to your PC.