The most awaited show on Indian Television, Peshwa Bajirao begins with the story of Peshwa Balaji Vishwanath Bhatt and his wife Radhabai. Balaji Vishwanath informs Radhabai that soon they would be blessed with a child who would become a great King in the future. The couple move out of their house in Chiplun when Mughal soldiers attack their village. Tararani Saheb is the queen of Chhatrapati Rajaram Bhonsle. On Rajarams death, his widow Tararani proclaims her infant son, Shivaji as Rajarams successor and herself as the regent.

Dhanaji requests Balaji Vishwanath to secretly meet Shahu who is held captive by the Mughals. Radhabai allows Balaji Vishwanath to go to the mission to rescue Shahu. Balaji Vishwanath secretly intrudes into Shahus tent. He learns that Shahu is not keeping well. On the other hand, Radhabai delivers a baby boy. Aurangzebs army captures Balaji Vishwanath and throws him off a cliff.

Balaji Vishwanath's relatives pronounce him dead. However, Radhabai refuses to declare herself as a widow. Balaji Vishwanath shows up and clears the confusion. Later, he informs Radhabai that he was rescued after being thrown off the cliff. Balaji and Radhabai name their child as Bajirao. A spiritual guru predicts Bajirao's early death.

Bajirao flips a coin which lands in the water. Radhabai rushes towards a waterfall to stop Bajirao. She gets shocked to see Bajirao jumping off the waterfall. When Bajirao steps out of the water, Radhabai grabs Bajirao by the ear and drags him to the house. She instructs Bajirao to not take unnecessary risks.

Bajirao plans to steal mangoes from Govindsheth's garden. Bajirao's teacher comes to his house and meets Radhabai. He tells Radhabai that Bajirao is not serious about his studies. Bajirao and his friends cleverly steal the mangoes from the garden and return home. Radhabai teaches a shloka to them. Later, she promises them to offer mango-juice if they recite the same shloka before her.

Bajiraos teacher punishes him for remaining absent from the school on the earlier day. Bajirao and his friends rush towards a river. Balaji Vishwanath plans to meet Kamruddin. Mughal soldiers stop Bajirao from going towards the river. Kamruddins son Nasir challenges Bajirao and his friends to play tug-of-war with an elephant.