The Hattiesburg Republican told The Clarion-Ledger that his proposed bill would also ban cellphone use unless a hands-free device is used.
Hudson said his bill, to be considered by the 2013 Legislature, would ban all mobile phone use by drivers younger than 18. Last year, a bill Hudson introduced died in committee.
Hudson said he wants the cellphone bill because it would be difficult for law enforcement to enforce a ban only on texting.
"We need to do something to protect people," he said. "We are losing too many people."
Mississippi Department of Public Safety spokesman Warren Strain says he was unfamiliar with Hudson's proposal, but he said the department favors proposals to improve road safety. Strain says inattentive driving is the leading cause of traffic accidents.
Mississippi, Missouri, New Mexico, Oklahoma and Texas have laws that ban only young drivers with learners permits from texting while driving. Six other states don't prohibit anyone from texting while driving.
The National Transportation Safety Board has urged states to ban all driver use of cellphones and other electronic devices, except in emergencies.
A 2011 NHTSA survey found nearly 90 percent of drivers have cellphones — a rate reflected in most ages and all income levels. The agency reviewed the rates at which drivers had used those phones while behind the wheel.
"Sending text messages or emailing while driving, while less frequent than talking on a cellphone while driving, was still quite high," according to NHTSA's report, which was the first national phone survey on distracted driving.
Mississippi now prohibits school bus drivers and those with learner's permits or intermediate licenses from text messaging while driving.
Hudson said he expects there will some bills filed this year that will seek only a ban on texting.
His proposal wouldn't apply to someone communicating with law enforcement, an emergency responder or E911 operator, a hospital, physician's office or health clinic.
A violation would be a misdemeanor and, upon conviction, punishable by a fine not to exceed $500. If the violation led to a motor vehicle accident, the maximum fine would go up to $1,000 in addition to any other fines or penalty.