#import "AppController.h"
#import <CoreFoundation/CoreFoundation.h>
#import <SystemConfiguration/SCNetworkReachability.h>

@implementation AppController

- (IBAction)checkConnection:(id)sender
{
	NSAlert *alert = [[[NSAlert alloc] init] autorelease];
	[alert setAlertStyle:NSInformationalAlertStyle];
	[alert addButtonWithTitle:@"Ok"];
	[alert setInformativeText:@"Connection Test"];
	
	const char *hostname = "google.com";
	SCNetworkConnectionFlags flags;
	if(SCNetworkCheckReachabilityByName(hostname, &flags))
	{
		if(kSCNetworkFlagsReachable & flags && !(kSCNetworkFlagsConnectionRequired & flags))
		{
			[alert setMessageText:@"You are connected!"];
			[alert runModal];
			return;
		}
	}
	[alert setMessageText:@"You are not connected!"];
	[alert runModal];
}
@end

Check Network Connection with SCNetworkCheckReachabilityByName

Objective C