The draft legislation, submitted to parliament by MP Waleed al-Tabtabai, proposes Iran-backed Hezbollah be classified a "terrorist organisation".
It also stipulates a jail term of between 10 and 20 years for members of Hezbollah and anyone who shows any form of loyalty to the group.
It also proposes jail terms of up to five years for anyone displaying Hezbollah's yellow logo or any symbol associated with the group.
The supreme court in Sunni-ruled Kuwait, which has a sizeable Shiite minority, last month convicted 21 Shiites of forming a "terrorist cell" with ties to Iran and Hezbollah and plotting attacks in the Gulf state.
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Last week, authorities expelled 15 Iranian diplomats and shut down the military, cultural and trade missions of the Iranian embassy in Kuwait over Tehran's backing of the "terrorist cell".
Iran said the allegation is baseless
Fourteen of the 21 convicted members are on the run. Local media said they fled to Iran by sea.
Around a third of Kuwait's native population of 1.35 million are Shiites.