Chris Urmson told delegates at the Ted (Technology, Entertainment and Design) conference that his eldest son was 11-years-old and due to take his driving test in "four and a half years".
"My team are committed to making sure that doesn't happen," he said.
He also laid out Google's commitment to fully automated cars.
Some automotive firms have opted to introduce driver-assist functions in cars in the hope that the technology can gradually win over the many sceptics who would be uncomfortable in a fully automated car.
By contrast Google's own car - a prototype electric pod revealed in December - will have no steering wheel or conventional controls although for early testing, extra controls will be fitted so one of Google's test drivers can take over if there is a problem.The view from Google's self-drive car and its computer during tests
The fact that people are driving more and getting stuck in traffic jams for longer were two other good reasons to roll the technology out as soon as possible, he said.
But, most importantly, self-drive cars could drastically reduce traffic accidents, he said.
"Some 1.2 million people are killed on the roads around the world each year. That number is equivalent to a jet falling out of the sky every day."
The incremental changes some car-makers are introducing are not enough, he said.
"That is not to say that driver-assistance cars won't be useful but if we are really going to make changes to our cities, get rid of parking lots, we need self-drive cars," he said.AI developments
Google's retrofitted self-drive cars have undergone extensive testing, racking up more than 700,000 miles on the road, and in 2013 were given to one hundred employees to test.
Mr Urmson shared with the Ted audience some of the more unusual traffic situations that the fleet of Google self-drive cars had encountered, including a child driving a toy car in the road and a woman in an electric wheelchair chasing a duck.
"There is nowhere in the handbook about how to deal with that situation," he said.
But, he added, the car slowed down and reacted appropriately in each case.
Some urge caution on the development of fully-automated cars.
Sven Beiker, executive director of the Center for Automotive Research at Stanford, has said that driverless cars may still require human input in extreme circumstances and that people may forget how to operate their vehicles if they do not do it regularly.AI debate
Mr Urmson was one of several speakers in a Ted session entitled "Machines that learn".
The head of Stanford's Artificial Intelligence Lab Dr Fei-Fei Li spoke about her project to develop visually-intelligent computers.
Using a database of millions of images taken from the internet, her team has taught a computer to both understand a picture and generate a short audio description of that image.
The Ted audience also heard two differing points of view on the growing debate about how damaging AI will be for humanity.
Philosopher Nick Bostrom urged those involved in building super-intelligent systems to make sure AI's "were motivated to pursue our values".
But Oren Etzioni, chief executive of the Allen Institute for Artificial Intelligence maintained that just because we are developing intelligent machines did not necessarily mean that they would operate autonomously.
"AIs will empower us and help us tackle the real problems that face humanity," he said.