"When Canadians have support - like family involvement in child care - it helps to drive our productivity and economic growth," Trudeau said at an event in Brampton, Ontario.
Most recent polls show the Liberals, the rival centre-left New Democrats and the ruling Conservatives all deadlocked at around 30 percent of the vote. If no party manages to break away, Canada looks set for a period of unstable minority government.
The ethnic vote is significant in Canada, which is home to significant Chinese, Indian, Italian, Filipino and Ukrainian communities.
The Liberals have traditionally favoured immigration and under Trudeau`s father, former Liberal Prime Minister Pierre Trudeau, Canada accepted well over a million people.
For decades it was assumed that newcomers to Canada would vote Liberal but since taking power in 2006, the Conservatives have tried hard to build ties to ethnic communities.
As a result they picked up dozens of seats, especially in the region around Toronto, which was one of the reasons Prime Minister Stephen Harper won a majority in the 2011 election.
Pollsters say the Liberals are much more competitive in the area surrounding Toronto, Canada`s largest city.
Under the Conservatives, who took power in 2006, Canada changed the immigration system to focus more on attracting skilled workers from abroad while slashing back programs that allowed family reunification.
Critics of the previous system said allowing in elderly relatives unnecessarily strained the healthcare and social security systems.
Trudeau said the Liberals would make the system more compassionate by doubling the number of applications allowed for parents and grandparents to 10,000 each year.
Defence Minister Jason Kenney, who as immigration minister spearheaded the drive to win Conservative support among immigrants, said doubling the applications made no sense unless the number of people allowed in was also increased.
"It`s a function of maths and I`d be quite happy to send Mr. Trudeau a calculator so he can figure that out," he told reporters.
Canada, home to 36 million, aims to attract 285,000 immigrants in 2015.