The Senate voted 40-6 Monday to approve the bill, which would make the use of a hand-held electronic device when behind the wheel a "primary offense."
The House of Delegates has approved a measure similar to the Senate bill.
The two houses have to pass identical versions before the legislation can go to the governor's desk, but Sen. James Robey, the Senate sponsor, said the differences between the bills are minor and he expects them to be worked out in a conference committee.
Raquel Guillory, a spokeswoman for Gov. Martin O'Malley, said that while the administration hasn't taken a position on the bill, the governor supported similar legislation in the past.
"It's not something we wouldn't sign," she said.
A dozen states and the District of Columbia have laws banning use of hand-held phones while driving; only Maryland and West Virginia have made it a secondary offense. According to the Department of Legislative Services, West Virginia will start enforcing its law as a primary offense in July.
The legislation is expected to increase the number of tickets issued for the violation in Maryland, where 7,894 citations were handed out for the offense in 2011.
The Senate bill would increase the maximum penalty for a violation from $40 to $75 for a first offense, $100 for a second offense and $175 for a third or subsequent offenses.
Robey, a Howard County Democrat and a former police chief, said distraction from cellphone use causes 1.2 million crashes a year in the United States. Those crashes cost an estimated $42 billion in lost wages, property damage and personal injuries, he said.
"A car is not a telephone booth on wheels," he said.
The legislature has come a long way on the issue of electronic distractions to drivers since Del. John S. Arnick, a Dundalk Democrat, introduced the first bill to ban the use of cellphones while driving in 1999. He kept proposing the measure without success until his death in 2006.
Lawmakers took their first step toward restricting use of electronic devices behind the wheel in 2009 when they adopted and O'Malley signed a ban on texting while driving.
A year later, when the legislature banned cellphone use while driving as a secondary offense, it did so only after a prolonged debate that ended in the bill's passage in the Senate by a 24-23 vote. That year, 10 of 12 Senate Republicans voted no. This year, GOP senators backed the measure by a 7-5 margin, and Sen. John Astle was the only Democrat opposed. There was no debate before the final vote.