Going by your screen cap you're apparently using your carrier's 4G cellular connection and not a WiFi connection. Is your browser also having this same issue with WiFi?
Try going to your Settings >> Application manager, find your browser app, and tap the 'Force stop' button and then the 'Clear cache' button. If you're still getting that error message after that, you might also want to just shut down your phone and re-seat your SIM card.
You might also want to try installing a cellular connection app like this one from OpenSignal
https://play.google.com/store/apps/details?id=com.staircase3.opensignal
or this Network Cell Info app
https://play.google.com/store/apps/details?id=com.wilysis.cellinfo&hl=en
Check the signal strength and approximate distance of the nearest cell tower.
Has this problem been happening a lot or did it just start up recently? Also, are any apps also having connectivity issues or is it just your browser?