My friend's gmail I'd is logged in my mobile I think he is monitoring my call logs ,is there any way to monitor my call logs?
From my experience with flashing different roms on different devices over the years, it is highly unlikely or even impossible that they are monitoring your call logs.
Google accounts do not keep track of your call logs unless you are a Google voice user. If your friends account is the primary Google account on the phone, they would have access to any information synced with Google from your device. I would be more worried about other information they could access such as your location, installed applications, synced contacts, etc.
Now if their account is only signed into your Gmail application, they would not have access to any information on your device.
I highly recommend removing their account from your system accounts. This can be done in system settings.
Settings > Accounts & Sync > Google > select friends account > Remove Account
For a little bit of background, I have found that the only way to access call logs on a device is to extract them with a third party app or by contacting the network carrier.