Iranian officials have said the country's missile programme was for deterrent purposes.
The bill includes Iran's countermeasure plans for any USA acts of exploitation and terrorism in the region, as well as the Western country's hostile moves that undermine the successful implementation of Iran's nuclear deal, dubbed JCPOC, which went into effect in January 2016.
The US legislation would impose mandatory penalties on people involved in Iran's ballistic missile program and anyone who does business with them.
After Larijani announced the vote results, lawmakers shouted: "Death to America".
The bill would allocate over $260 million each to Iran's ballistic missile program and the Quds Force - the external arm of the Islamic Revolutionary Guard Corps - which is deployed to Iraq and Syria.
The bill secured 240 yes votes and one abstention.
Sanctions against Iran is mainly in response to Tehran's growing missile programme.
Washington's new sanctions violate a 2015 nuclear deal with Iran both "in letter and spirit".
Trump repeatedly threatened to tear up what he once called "the worst deal ever", but last month he backed away from a key campaign promise to withdraw from the nuclear agreement.
Deputy Iranian Foreign Minister Abbas Araqchi is seen walking in Majlis (Iranian Parliament) on August 13, 2017.
"The bill has very wisely tried not to violate the JCPOA and also give no chance to the other party to manipulate it, " Araqchi said.
"Iran boasts potential and actual options to confront hostile United States actions".
Araghchi, also in defense, said the countermeasure bill is "much stronger" than US Congress bill against Iran, since it also extends support to the Islamic Republic's armed forces and all related ministries.
Tehran's sanctions aim to ban such persons from entering Iran, confiscate their assets within the powers of the Islamic republic, and block their financial transactions.