Correct position of hands on flat handlebars I have had a numbing sensation in my thumbs. I take it it is caused by the pressure of holding the handlebars while riding. The bike is a Schwinn Signature M3030 - SR SUNTOUR mountain bike.
Could be the position of yours hands, which you can adjust yourself, but is more likely a combination of the over all bike fit. Things such as seat position, handlebar height and a variety of other things all play a part in how much pressure your hands exert onto the handlebars. Riding a bike that is too large can have your body leaning to much on the bars and exerting too much force on your hands and wrists.

Depending on what grip you currently use you might try changing them to something a bit softer such as some of the silicone variety, ESI or similar for example. Sometime gel padded gloves can help but I would venture to guess that it is a bit more complex and probably related to the over all fit of the bike. 

If you ride often numbness is definitely something you should take seriously and if it is worth the money and you do ride often, you may think about having a proper fit done at a shop or at very least take your bike in and explain the problem and get their opinion. 

Also, make sure you are not gripping the bike too hard, sounds silly but it is possible, your grip should be firm but semi relaxed, not holding on for dear life sort of grip. 

Lastly, the angle of your wrists can also be a factor, depending on what type of shifters/brake lever you have you might try adjusting them downward or upward to try and find a more comfortable and natural position.