The measure will go before the Assembly's Women and Children Committee on Monday.
A 2006 state law bans tanning bed use by anyone under 14, and requires written parental consent for those ages 14 to 17.
The issue has seen renewed interest after a Nutley woman was accused this month of taking her 5-year-old daughter into a tanning booth. That allegedly resulted in burns to the child's skin, and the woman has pleaded not guilty to child endangerment.
A similar measure was approved by a state Assembly panel and the full Senate last year.
California and Vermont are the only states that now ban tanning for children under age 18.
