Speaking before students packed into a library at East High School in Des Moines, Biden also spoke of new ways to support teachers, including providing incentives to keep them in the classroom.
The Delaware senator said he plans "on being the education president unlike any president has in American history."
"The reason I say that is I believe, absolutely positively, that (education) is the key to our security - economic, militarily and political," Biden said.
He said his parents didn't attend college, but they always encouraged him to go.
His mother, he said, would tell him "'Joey, children tend to become that what you expect of them,' and we're not expecting enough of you," Biden told the crowd. "I expect much more."
Biden's plan would add two years of preschool to the public school system. It would fully fund Head Start and other early childhood programs, and expand education and nutrition programs that begin at birth. Biden said he believes the earlier children start their education, the better prepared they will be for life.
"You've got to start kids at school early. We've gotta give them a better chance," he said.
Each year in the United States, 400,000 students who qualify for college don't go because of the cost, according to Biden's campaign. He said he wants that to change.
"Every single one of you should be able to go," he told the students, many holding campaign signs.
Under his plan, he encourages families and schools to begin talking about how they'll finance a child's education as early as the eighth grade.
Biden said he wants all Americans to have access to college. He proposed credits and grants up to $12,000 per child to help cover the average costs at a two-year-college, or half of the average costs at a four-year college. His plan would also allow families to claim tax credits for more than one child per year.
In addition, Biden proposed expanding the maximum amount available in Pell Grants from $4,310 a year to $6,300. Legislation signed by President Bush in September would increase the current amount to $5,400 by 2012.
Biden proposed hiring an additional 100,000 teachers to help reduce class size, aimed at average classes of 18 students. The federal government would assist states in doing so by providing $2 billion a year in grants to attract more teachers and pay for incentives. He added that teachers should be able to start their careers at a minimum of $45,000 per year.
"We don't pay teachers enough, we don't attract the best teachers," he said.
New teachers would get a bonus if they committed to teaching at the same school for five years, and they'd get help paying student loans. Those who teach in high-need schools should get bonuses as well, Biden said.
"This should not be the only profession where we rely on people coming to it only if they are totally dedicated and willing not to do as well (monetarily) as their fellow graduates," he said.
His plan would cost about $30 billion a year - an amount he said is less than the country spends for three months of the Iraq war.
Biden said his plan would succeed where No Child Left Behind has failed.
"The essence of No Child Left Behind is how to measure success. What I'm talking about today is how to promote success," he said.