When you replace a dripping faucet and the newly installed one still drips, the cause is usually a piece of something that got into the pipe during the installation. You need to flush out the pipe.
Turn off the water and remove the valve stem that is leaking. Take a bucket and hold it upside down over the open valve. Have someone turn on the water full force so that the water will come gushing up through the valve. Use the bucket to direct the water back into the sink. (If you don't have the bucket in place you will water the ceiling.)
It only takes a few seconds to flush out the line. Before putting the faucet back together, check that the washer wasn't damaged during the installation. Then put it all back together and check for the drip. If it is still dripping, there could be a defective "seat", the part of the valve the washer pushes against. This can be removed and replaced using a "seat wrench".