The incident took place in Pakkabagh area of the Uttar Pradesh capital late on Wednesday.
Vimla dragged her children Ram Kishore, 5, and Kamal Kishore, 3, who were playing outside their house, to the roof and beat them up with bricks for over 10 minutes.
Police said the neighbours heard the children cry and rushed to their rescue. They found the children in a pool of blood. Ram Kishore died on the spot, while the younger one died at the hospital.
Kamlesh, the distraught father, told the police that during the seven years of their marriage, Vimla had lost temper on many occasions.
Police officer Samar Bahadur Singh told IANS that the woman has been arrested and booked for murder.