The legislation could have significant local impact because many area contractors have complained of a critical shortage of plumbers, carpenters, electricians and other well-trained crafts people.
Some have said they have had to turn away work because they don't have enough qualified people.
The vote followed a debate on the House floor during which opponents charged developers and contractors, not aspiring apprentices, would benefit from the program because they would receive grants from the state of up to $1,000 a year for each apprentice.
"In many respects, this legislation is welfare for the business community and a big subsidy for those particular groups," said Del. Clarence Davis, D-Baltimore.
Others defended the bill, saying it would provide a boost to young people seeking career skills, especially those in poorer areas of the state, while helping ease the worker shortage.
"This will give us an opportunity to make big advances in that arena," said Del. Adelaide C. Eckardt, R-Dorchester.
The legislation now goes to the state Senate, where a similar bill from Poole was defeated last year, mainly because of its cost. The program would cost taxpayers $1.86 million during its first year, according to the Department of Legislative Services.
Poole said he expects opposition in the Senate again, but will do his best to get the bill through.