Naram Garam is the story of Kusum (Swaroop Sampat) and her father (A.K. Hangal), who are left homeless due to non-repayment of debts from the local money lender. They are helped by Ramprasad (Amol Palekar), who is in love with Kusum. Bhavani Shankar (Utpal Dutt), Ramprasad's employer, is feared by his family members and employees, but is himself terrified of his own mother-in-law (Dina Pathak). Ramprasad helps Bhavani Shankar get the possession of his ancestral home after a 53-year-long legal battle with a squatter and is therefore assigned the responsibility of getting the house back in shape so that it can be re-occupied. In the meanwhile, Kusum and her father come to the shelter of Ramprasad and start staying in the house. Ramprasad doesn't have a house of his own, hence decides to let them stay illegally until he can find an alternative.

When this comes to the knowledge of the estate manager, Gajanan Babu (Suresh Chatwal), he arrives furious and determined to oust the squatters. However, he succumbs to the charms of Kusum and instead of ousting the old man and his daughter, presents a proposal of marriage. Horrified, Kusum and Ramprasad turn to Kali Shankar, a.k.a. Babua (Shatrughan Sinha), Bhavani Shankar's younger brother, for help. Babua is a garage mechanic and a ruffian with a kind heart for women in distress. He successfully dissuades Gajanan Babu from carrying through with his proposal, but is also determined to oust Kusum and her father. However, he too is captivated by Kusum's beauty and presses his suit. Then Ramprasad finally turns to Bhavani Shankar, who dissuades Babua using his younger brother's fear of hi