I am using 50 mm 1.8 potrait lens with my canon 600D. But when i take a portrait with f1.8 on Av mode using autofocus, only subjects eyes are sharp and rest of the other face is slightly blurry. How to overcome this?
You can try other apertures, such as f/2, f/2.2, and f/2.5 to see if they give you the Depth of Field (DoF) you want. If you want to keep the background blurred after stopping down then increase the separation between your subject and the background.
If that doesn't solve the problem, you may be experiencing a front-focus issue. If the parts of the face behind the eyes were in better focus than the eyes themselves, it might be a back-focus issue. Unfortunately, the 600D is not capable of user controlled Auto Focus Micro Adjustment that is available in higher end bodies such as the 7D, 70D, and 5D3. Your camera and lens together will need to be calibrated by a Canon Service Center if they need to be adjusted.
Use a slower aperture setting. What you are encountering is Depth of Field and is normal. You can use any of numerous depth of field calculators to determine the setting you need. Depth of field is primarily determined by focal length, distance to subject and aperture. Since you have a fixed focal length, you can either get further away from the subject or use a slower aperture.
Focus stacking is also an option in some cases, but generally a slower aperture is a better solution since focus stacking requires a stationary object and shutter speed doesn't particularly matter when the subject is stationary.